1. POLYNOMIALS
Ms. Johnson 8th Grade Math

2. KEY VOCABULARY
 Variable- A quantity that can change or vary,
taking on different values

3. KEY VOCABULARY
 Variable- A quantity that can change or vary, taking on
different values
Constant- A quantity having a fixed
value that does not change or vary, such
as a number. A constant term does not
contain a variable.
[( y= 5 + x ) in this example, 5 is a
constant

4. KEY VOCABULARY
 Variable- A quantity that can change or vary, taking
on different values
 Constant- A quantity having a fixed value that does
not change or vary, such as a number. A constant term
does not contain a variable.
[( y= 5 + x ) in this example, 5 is a constant
Coefficient- A number that multiplies a
variable [ (4b) in this example, 4 is a
coefficient]

5. KEY VOCABULARY
 Variable- A quantity that can change or vary, taking on
different values
 Constant- A quantity having a fixed value that does not
change or vary, such as a number. A constant term does not
contain a variable.
[( y= 5 + x ) in this example, 5 is a constant
 Coefficient- A number that multiplies a variable [ (4b) in
this example, 4 is a coefficient]
 Like Terms- Terms whose variables and
exponents are the same (the coefficients can
be different) [5a + 8a ; or x2y + 3x2y]

6. KEY VOCABULARY
 Monomial- a polynomial containing one term which
may be a number, a variable, or a product of numbers
and variables, with no negative or fractional exponents
( -5, xy, 5x2, 5x2y3z )

7. KEY VOCABULARY
 Monomial- a polynomial containing one term which
may be a number, a variable, or a product of numbers
and variables, with no negative or fractional exponents
( -5, xy, 5x2, 5x2y3z )
 Binomial- a polynomial containing two unlike terms
( x+ 5, xy + 5, 5x2 – x, 5x2 + y3)

8. KEY VOCABULARY
 Monomial- a polynomial containing one term which
may be a number, a variable, or a product of numbers
and variables, with no negative or fractional exponents
( -5, xy, 5x2, 5x2y3z )
 Binomial- a polynomial containing two unlike terms
( x+ 5, xy +5, 5x2 – x, 5x2 + y3)
 Trinomial- a polynomial containing three unlike
terms
(x+5+y, 5x2 –x+y, 5x2 + y3 – z)

9. KEY VOCABULARY
 Monomial- a polynomial containing one term which may
be a number, a variable, or a product of numbers and
variables, with no negative or fractional exponents
( -5, xy, 5x2, 5x2y3z )
 Binomial- a polynomial containing two unlike terms
( x+ 5, xy+5, 5x2 – x, 5x2 + y3)
 Trinomial- a polynomial containing three unlike terms
(x+5+y, 5x2 –x+y, 5x2 + y3 – z)
 Polynomial- an expression that is a monomial or the sum
of monomials (xy, xy- 5 , 5x2 – x + y, 5x2 + y3 – z +3)

10. 8.A.6 MULTIPLY MONOMIALS
 Just remember the Product Law!
12a3b2 (3a4b6)
Product Law2 applies to the coefficients
Product Law1 applies to the variables
121a3b2 (31a4b6) =

11. 8.A.6 MULTIPLY MONOMIALS
 Just remember the Product Law!
12a3b2 (3a4b6)
Product Law2 applies to the coefficients
Product Law1 applies to the variables
121a3b2 (31a4b6) = 361a7b8 = 36a7b8

12. 8.A.6 MULTIPLY MONOMIALS
 Some examples:
a. 5bc (4b3c2) =
20b4c3
*don’t forget about the hidden ones
b. 4a3mr (6am4) =
24a4m5r
*if a variable only appears once, keep it in the final answer
c. -2b3m4 (3b2m-2) =
*don’t forget about integer rules!
d. 12a4bg3 (-2abg3) =
-6b5m2
-24a5b2g6

13. 8.A.6 MULTIPLY MONOMIALS
 Now You Try Some!
a) 4a3m (8a4m6)
b) 5c4a3 (-3c2a)
c) -6m4r-2 (3m0r6)
d)2b6 (8b3c)

14. 8.A.6 MULTIPLY MONOMIALS
 Now You Try Some!
a) 4a3m (8a4m6) = 32a7m7
b) 5c4a3 (-3c2a)
c) -6m4r-2 (3m0r6)
d)2b6 (8b3c)

15. 8.A.6 MULTIPLY MONOMIALS
 Now You Try Some!
a) 4a3m (8a4m6) = 32a7m7
b) 5c4a3 (-3c2a) = -15a4c6
c) -6m4r-2 (3m0r6)
d)2b6 (8b3c)

16. 8.A.6 MULTIPLY MONOMIALS
 Now You Try Some!
a) 4a3m (8a4m6) = 32a7m7
b) 5c4a3 (-3c2a) = -15a4c6
c) -6m4r-2 (3m0r6) = -18m4r4
d)2b6 (8b3c)

17. 8.A.6 MULTIPLY MONOMIALS
 Now You Try Some!
a) 4a3m (8a4m6) = 32a7m7
b) 5c4a3 (-3c2a) = -15a4c6
c) -6m4r-2 (3m0r6) = -18m4r4
d)2b6 (8b3c) = 16b9c

18. 8.A.6 DIVIDE MONOMIALS
 Just remember the quotient laws!
27a5b6 ÷ 9a2b
Quotient Law2 let’s us divide 27 by 9 = 3
Quotient Law1 lets us divide the variables

19. 8.A.6 DIVIDE MONOMIALS
 Just remember the quotient laws!
27a5b6 ÷ 9a2b
Quotient Law2 let’s us divide 27 by 9 = 3
Quotient Law1 lets us divide the variables (which
means subtract the exponents for each variable)
= 3a3b5

20. 8.A.6 DIVIDE MONOMIALS
 Some Examples:
a)4a6b3 ÷ 2a3b
a)12m4n2 ÷ 4mn5
a)2a5b3 ÷ 3a3
b)5m7c4 ÷ 5m7c-9

21. 8.A.6 DIVIDE MONOMIALS
 Some Examples:
a)4a6b3 ÷ 2a3b = 2a3b2
a)12m4n2 ÷ 4mn5
a)2a5b3 ÷ 3a3
b)5m7c4 ÷ 5m7c-9

22. 8.A.6 DIVIDE MONOMIALS
 Some Examples:
a)4a6b3 ÷ 2a3b = 2a3b2
a)12m4n2 ÷ 4mn5 = 3m3n-3
a)2a5b3 ÷ 3a3
a)5m7c4 ÷ 5m7c-9

23. 8.A.6 DIVIDE MONOMIALS
 Some Examples:
a)4a6b3 ÷ 2a3b = 2a3b2
a)12m4n2 ÷ 4mn5 = 3m3n-3
a)2a5b3 ÷ 3a3 = (2/3) a2b3
a)5m7c4 ÷ 5m7c-9

24. 8.A.6 DIVIDE MONOMIALS
 Some Examples:
a)4a6b3 ÷ 2a3b = 2a3b2
a)12m4n2 ÷ 4mn5 = 3m3n-3
a)2a5b3 ÷ 3a3 = (2/3) a2b3
5m7c4 ÷ 5m7c-9 = 1m0c13

25. 8.A.6 DIVIDE MONOMIALS
 Some Examples:
a)4a6b3 ÷ 2a3b = 2a3b2
a)12m4n2 ÷ 4mn5 = 3m3n-3
a)2a5b3 ÷ 3a3 = (2/3) a2b3
a)5m7c4 ÷ 5m7c-9 = 1m0c13 = c13

26. 8.A.6 DIVIDE MONOMIALS
 Now You Try Some…Alone!
a) 30a6 ÷ 5a
a) 32b4m3 ÷ 8bm3
a) 16a7c3 ÷ 4a9
 9b6r5 ÷ 6b2r-4

27. 8.A.6 DIVIDE MONOMIALS
 Now You Try Some…Alone!
a) 30a6 ÷ 5a = 6a5
a) 32b4m3 ÷ 8bm3
a) 16a7c3 ÷ 4a9
 9b6r5 ÷ 6b2r-4

28. 8.A.6 DIVIDE MONOMIALS
 Now You Try Some…Alone!
a) 30a6 ÷ 5a = 6a5
a) 32b4m3 ÷ 8bm3 = 4b3m0
a) 16a7c3 ÷ 4a9
a) 9b6r5 ÷ 6b2r-4

29. 8.A.6 DIVIDE MONOMIALS
 Now You Try Some…Alone!
a) 30a6 ÷ 5a = 6a5
a) 32b4m3 ÷ 8bm3 = 4b3m0 = 4b3
a) 16a7c3 ÷ 4a9
a) 9b6r5 ÷ 6b2r-4

30. 8.A.6 DIVIDE MONOMIALS
 Now You Try Some…Alone!
a) 30a6 ÷ 5a = 6a5
a) 32b4m3 ÷ 8bm3 = 4b3m0 = 4b3
a) 16a7c3 ÷ 4a9 = 4a-2c3
a) 9b6r5 ÷ 6b2r-4

31. 8.A.6 DIVIDE MONOMIALS
 Now You Try Some…Alone!
a) 30a6 ÷ 5a = 6a5
a) 32b4m3 ÷ 8bm3 = 4b3m0 = 4b3
a) 16a7c3 ÷ 4a9 = 4a-2c3
a) 9b6r5 ÷ 6b2r-4 = (3/2)b4r9

32. 8.A.9- DIVIDE A POLYNOMIAL BY A
MONOMIAL
 This works a lot like Dividing a monomial by a
monomial
15a4b7 + 6a2b4
3ab
Break this into two separate fractions:

33. 8.A.9- DIVIDE A POLYNOMIAL BY A
MONOMIAL
 This works a lot like Dividing a monomial by a
monomial
15a4b7 + 6a2b4
3ab
Break this into two separate fractions:

34. 8.A.9- DIVIDE A POLYNOMIAL BY A
MONOMIAL
 This works a lot like Dividing a monomial by a
monomial
15a4b7 + 6a2b4
3ab
Break this into two separate fractions:

35. 8.A.9- DIVIDE A POLYNOMIAL BY A
MONOMIAL
15a4b7 + 6a2b4
3ab
Break this into two separate fractions:
15a4b7 = 6a2b4 =
3ab 3ab

36. 8.A.9- DIVIDE A POLYNOMIAL BY A
MONOMIAL
15a4b7 + 6a2b4
3ab
Now follow Quotient Laws!
15a4b7 = 5a3b6 6a2b4 = 2ab3
3ab 3ab

37. 8.A.9- DIVIDE A POLYNOMIAL BY A
MONOMIAL
15a4b7 = 5a3b6 6a2b4 = 2ab3
3ab 3ab
Put these two parts together, using the
operation from the original! In this case, it
was an addition problem, so the answer is…
5a3b6 + 2ab3

38. 8.A.9- DIVIDE A POLYNOMIAL BY A
MONOMIAL
 One more example:
A. 18m6n9 − 24m4n7
6m2n3

39. 8.A.9- DIVIDE A POLYNOMIAL BY A
MONOMIAL
 One more example:
A. 18m6n9 − 24m4n7
6m2n3
*break into two fractions!
18m6n9 = 24m4n7 =
6m2n3 6m2n3

40. 8.A.9- DIVIDE A POLYNOMIAL BY A
MONOMIAL
 One more example:
A. 18m6n9 − 24m4n7
6m2n3
Follow quotient laws!
18m6n9 = 3m4n6 24m4n7 =
6m2n3 6m2n3

41. 8.A.9- DIVIDE A POLYNOMIAL BY A
MONOMIAL
 One more example:
A. 18m6n9 − 24m4n7
6m2n3
Follow quotient laws
18m6n9 = 3m4n6 24m4n7 = 4m2n4
6m2n3 6m2n3

42. 8.A.9- DIVIDE A POLYNOMIAL BY A
MONOMIAL
 One more example:
A. 18m6n9 − 24m4n7
6m2n3
*follow quotient laws!
18m6n9 = 3m4n6 24m4n7 = 4m2n4
6m2n3 6m2n3
*put it all together:
3m4n6 − 4m2n4

43. 8.A.9- DIVIDE A POLYNOMIAL BY A
MONOMIAL
 Now You Try Alone ! And don’t forget integer
rules!
A.30a6b2 − 27a4b6
3a3b4
B. 28m5n3p4 + 32m2n5p
4mn7p3

44. 8.A.9- DIVIDE A POLYNOMIAL BY A
MONOMIAL
 Let’s Go Over Them!
A.30a6b2 − 27a4b6
3a3b4
30a6b2 = 27a4b6 =
3a3b4 3a3b4

45. 8.A.9- DIVIDE A POLYNOMIAL BY A
MONOMIAL
 Let’s Go Over Them!
A.30a6b2 − 27a4b6
3a3b4
30a6b2 = 10a3b-2 27a4b6 =
3a3b4 3a3b4

46. 8.A.9- DIVIDE A POLYNOMIAL BY A
MONOMIAL
 Let’s Go Over Them!
A.30a6b2 − 27a4b6
3a3b4
30a6b2 = 10a3b-2 27a4b6 = 9ab2
3a3b4 3a3b4

47. 8.A.9- DIVIDE A POLYNOMIAL BY A
MONOMIAL
 Let’s Go Over Them!
A. 30a6b2 − 27a4b6
3a3b4
30a6b2 = 10a3b-2 27a4b6 = 9ab2
3a3b4 3a3b
10a3b-2 − 9ab2

48. 8.A.9- DIVIDE A POLYNOMIAL BY A
MONOMIAL
 Now You Try! And don’t forget integer rules!
B. 28m5n3p4 + 32m2n5p
4mn7p3

49. 8.A.9- DIVIDE A POLYNOMIAL BY A
MONOMIAL
 Let’s Go Over Them!
B. 28m5n3p4 + 32m2n5p
4mn7p3
*Break into 2 fractions
28m5n3p4 32m2n5p
4mn7p3 4mn7p3

50. 8.A.9- DIVIDE A POLYNOMIAL BY A
MONOMIAL
 Let’s Go Over Them!
B. 28m5n3p4 + 32m2n5p
4mn7p3
*Break into 2 fractions
28m5n3p4 = 7m4n-4p 32m2n5p =
4mn7p3 4mn7p3

51. 8.A.9- DIVIDE A POLYNOMIAL BY A
MONOMIAL
 Let’s Go Over Them!
B. 28m5n3p4 + 32m2n5p
4mn7p3
*Break into 2 fractions
28m5n3p4 = 7m4n-4p 32m2n5p = 8mn-2p-2
4mn7p3 4mn7p3

52. 8.A.9- DIVIDE A POLYNOMIAL BY A
MONOMIAL
 Let’s Go Over Them!
B. 28m5n3p4 + 32m2n5p
4mn7p3
*Break into 2 fractions
28m5n3p4 = 7m4n-4p 32m2n5p = 8mn-2p-2
4mn7p3 4mn7p3
7m4n-4p + 8mn-2p-2

53. 8.A.9- DIVIDE A POLYNOMIAL BY A
MONOMIAL
 On loose leaf! On your own! Show the broken up
fractions!
1. 36a5b7 + 12a3b4
6ab4
2. 21c8d4 − 35c9d
7c8d3
3. 40a6c5 + 60a2c7
20ac4

54. 8.A.9- DIVIDE A POLYNOMIAL BY A
MONOMIAL
 Let’s go over them…
1. 36a5b7 + 12a3b4 = 6a4b3 + 2a2
6ab4
2. 21c8d4 − 35c9d
7c8d3
3. 40a6c5 + 60a2c7
20ac4

55. 8.A.9- DIVIDE A POLYNOMIAL BY A
MONOMIAL
 Let’s go over them…
1. 36a5b7 + 12a3b4 = 6a4b3 + 2a2
6ab4
2. 21c8d4 − 35c9d = 3d − 5cd-2
7c8d3
3. 40a6c5 + 60a2c7
20ac4

56. 8.A.9- DIVIDE A POLYNOMIAL BY A
MONOMIAL
 Let’s go over them…
1. 36a5b7 + 12a3b4 = 6a4b3 + 2a2
6ab4
2. 21c8d4 − 35c9d = 3d − 5cd-2
7c8d3
3. 40a6c5 + 60a2c7 = 2a5c + 3ac3
20ac4

57. 8.A.8- MULTIPLY A BINOMIAL BY A
MONOMIAL
 5(4 + 7) =
There are two ways to evaluate this equation.
1. PEMDAS
1. Distributive Property 5(4+7)

58. 8.A.8- MULTIPLY A BINOMIAL BY A
MONOMIAL
 5(4 + 7) =
There are two ways to evaluate this equation.
1. PEMDAS
Parentheses: 4+7 =11
1. Distributive Property 5(4+7)

59. 8.A.8- MULTIPLY A BINOMIAL BY A
MONOMIAL
 5(4 + 7) =
There are two ways to evaluate this equation.
1. PEMDAS
Parentheses: 4+7 =11
Multiplication: 5(11) = 55
1. Distributive Property 5(4+7)

60. 8.A.8- MULTIPLY A BINOMIAL BY A
MONOMIAL
 5(4 + 7) =
There are two ways to evaluate this equation.
1. PEMDAS
Parentheses: 4+7 =11
Multiplication: 5(11) = 55
1.Distributive Property 5(4+7) = 5(4) +

61. 8.A.8- MULTIPLY A BINOMIAL BY A
MONOMIAL
 5(4 + 7) =
There are two ways to evaluate this equation.
1. PEMDAS
Parentheses: 4+7 =11
Multiplication: 5(11) = 55
1. Distributive Property 5(4+7) = 5(4) + 5(7)

62. 8.A.8- MULTIPLY A BINOMIAL BY A
MONOMIAL
 5(4 + 7) =
There are two ways to evaluate this equation.
1. PEMDAS
Parentheses: 4+7 =11
Multiplication: 5(11) = 55
1. Distributive Property 5(4+7) = 5(4) + 5(7)
= 20 + 35

63. 8.A.8- MULTIPLY A BINOMIAL BY A
MONOMIAL
 5(4 + 7) =
There are two ways to evaluate this equation.
1. PEMDAS
Parentheses: 4+7 =11
Multiplication: 5(11) = 55
1. Distributive Property 5(4+7) = 5(4) + 5(7)
= 20 + 35
= 55

64. 8.A.8- MULTIPLY A BINOMIAL BY A
MONOMIAL
 Remember the Distributive Property (the
milkman delivers to each house separately):
a(b + c) = ab +ac
5(c − 6d) =
-4a(7 + 6d) =

65. 8.A.8- MULTIPLY A BINOMIAL BY A
MONOMIAL
 Remember the Distributive Property (the
milkman delivers to each house separately):
a(b + c) = ab +ac
5(c − 6d) = 5c
-4a(7 + 6d) =

66. 8.A.8- MULTIPLY A BINOMIAL BY A
MONOMIAL
 Remember the Distributive Property (the
milkman delivers to each house separately):
a(b + c) = ab +ac
5(c − 6d) = 5c − 30d
and these are not like terms, so this is the
final answer!
-4a(7 + 6d) =

67. 8.A.8- MULTIPLY A BINOMIAL BY A
MONOMIAL
 Remember the Distributive Property (the
milkman delivers to each house separately):
a(b + c) = ab +ac
5(c − 6d) = 5c − 30d
and these are not like terms, so this is the
final answer!
-4a(7 + 6d) = -28a

68. 8.A.8- MULTIPLY A BINOMIAL BY A
MONOMIAL
 Remember the Distributive Property (the
milkman delivers to each house separately):
a(b + c) = ab +ac
5(c − 6d) = 5c − 30d
and these are not like terms, so this is the
final answer!
-4a(7 + 6d) = -28a − 24ad

69. 8.A.8- MULTIPLY A BINOMIAL BY A
MONOMIAL
 Some Examples:
1.5z(a2 − 3b)
1.4r3(8r + 7)
1.6b2(7b + 3b)

70. 8.A.8- MULTIPLY A BINOMIAL BY A
MONOMIAL
 Some Examples:
1.5z(a2 − 3b) = 5za2 − 15zb
1.4r3(8r + 7)
1.6b2(7b + 3b)

71. 8.A.8- MULTIPLY A BINOMIAL BY A
MONOMIAL
 Some Examples:
1.5z(a2 − 3b) = 5za2 − 15zb
2.4r3(8r + 7) = 32r4 + 28r3
Don’t forget about product law! These aren’t like terms!!
1.6b2(7b + 3b)

72. 8.A.8- MULTIPLY A BINOMIAL BY A
MONOMIAL
 Some Examples:
1.5z(a2 − 3b) = 5za2 − 15zb
2.4r3(8r + 7) = 32r4 + 28r3
Don’t forget about product law! These aren’t like terms!!
1.6b2(7b + 3b)= 42b3 + 18b3

73. 8.A.8- MULTIPLY A BINOMIAL BY A
MONOMIAL
 Some Examples:
1.5z(a2 − 3b) = 5za2 − 15zb
2.4r3(8r + 7) = 32r4 + 28r3
Don’t forget about product law! These aren’t like terms!!
1.6b2(7b + 3b)= 42b3 + 18b3 = 60b3
These are like terms!

74. 8.A.8- MULTIPLY A BINOMIAL BY A
MONOMIAL
 Now you try some… ALONE!
1. -4c(7 − 6d)
2.8m(6m4 + m5)
3. -7a(4 − a)
4.9b3 (7ab − 4ab4)

75. 8.A.8- MULTIPLY A BINOMIAL BY A
MONOMIAL
 Now you try some… ALONE!
1. -4c(7 − 6d) = -28c + 24cd
2.8m(6m4 + m5)
3. -7a(4 − a)
4.9b3 (7ab − 4ab4)

76. 8.A.8- MULTIPLY A BINOMIAL BY A
MONOMIAL
 Now you try some… ALONE!
1. -4c(7 − 6d) = -28c + 24cd
*NB: a negative times a negative is a positive
1.8m(6m4 + m5)
2. -7a(4 − a)
3.9b3 (7ab − 4ab4)

77. 8.A.8- MULTIPLY A BINOMIAL BY A
MONOMIAL
 Now you try some… ALONE!
1. -4c(7 − 6d) = -28c + 24cd
*NB: a negative times a negative is a positive
 8m(6m4 + m5) = 48m5 + 8m6
 -7a(4 − a)
 9b3 (7ab − 4ab4)

78. 8.A.8- MULTIPLY A BINOMIAL BY A
MONOMIAL
 Now you try some… ALONE!
1. -4c(7 − 6d) = -28c + 24cd
*NB: a negative times a negative is a positive
1.8m(6m4 + m5) = 48m5 + 8m6
2. -7a(4 − a) = -28a +7a2
3.9b3 (7ab − 4ab4)

79. 8.A.8- MULTIPLY A BINOMIAL BY A
MONOMIAL
 Now you try some… ALONE!
1. -4c(7 − 6d) = -28c + 24cd
*NB: a negative times a negative is a positive
1.8m(6m4 + m5) = 48m5 + 8m6
2. -7a(4 − a) = -28a +7a2
3.9b3 (7ab − 4ab4) = 63ab4 − 36ab7

80. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
(n+4) (n−5)
For problems like this, we will learn
about an important acronym : FOIL
Basically you use the distributive
property twice.

81. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
(n+4) (n−5)

82. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
(n+4) (n−5)
F- firsts n  n = n2

83. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
(n+4) (n−5)
F- firsts n  n = n2
O- outers n  -5 = -5n

84. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
(n+4) (n−5)
F- firsts n  n = n2
O- outers n  -5 = -5n
I- inners 4  n = 4n

85. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
(n+4) (n−5)
F- firsts n  n = n2
O- outers n  -5 = -5n
I- inners 4  n = 4n
L- lasts 4  -5 = -20

86. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
(n+4) (n−5)
F- firsts n  n = n2
O- outers n  -5 = -5n like terms
I- inners 4  n = 4n = -n
L- lasts 4  -5 = -20

87. 8.A.7 ADD AND SUBTRACT
POLYNOMIALS
(n+4) (n−5)
F- firsts n  n = n2
O- outers n  -5 = -5n like terms
I- inners 4  n = 4n = -n
L- lasts 4  -5 = -20
So final answer: n2 − n − 20
(the signs become the operators!)

88. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
(a+2) (a+6)

89. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
(a+2) (a+6)
F- firsts a  a= a2

90. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
(a+2) (a+6)
F- firsts a  a = a2
O- outers a  6 = 6a

91. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
(a+2) (a+6)
F- firsts a  a = a2
O- outers a  6 = 6a
I- inners 2  a = 2a

92. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
(a+2) (a+6)
F- firsts a  a = a2
O- outers a  6 = 6a
I- inners 2  a = 2a
L- lasts 2  6 = 12

93. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
(a+2) (a+6)
F- firsts a  a = a2
O- outers a  6 = 6a like terms
I- inners 2  a = 2a = 8a
L- lasts 2  6 = 12

94. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
(a+2) (a+6)
F- firsts a  a = a2
O- outers a  6 = 6a like terms
I- inners 2  a = 2a = 8a
L- lasts 2  6 = 12
So final answer: a2 + 8a + 12
(the signs become the operators!)

95. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
1. (a+3)(a−5)
2. (b−4)(b−3)
3. (c+6)(c−4)
4. (d−5)(d+5)
5. (3e+4)(2e−2)

96. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
1. (a+3)(a−5) = a2 − 2a − 15
2. (b−4)(b−3)
3. (c+6)(c−4)
4. (d−5)(d+5)
5. (3e+4)(2e−2)

97. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
1. (a+3)(a−5) = a2 − 2a − 15
2. (b−4)(b−3) = b2 − 7b + 12
3. (c+6)(c−4)
4. (d−5)(d+5)
5. (3e+4)(2e−2)

98. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
1. (a+3)(a−5) = a2 − 2a − 15
2. (b−4)(b−3) = b2 − 7b + 12
3. (c+6)(c−4) = c2 + 2c − 24
4. (d−5)(d+5)
5. (3e+4)(2e−2)

99. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
1. (a+3)(a−5) = a2 − 2a − 15
2. (b−4)(b−3) = b2 − 7b + 12
3. (c+6)(c−4) = c2 + 2c − 24
4. (d−5)(d+5) = d2 − 25
5. (3e+4)(2e−2)

100. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
1. (a+3)(a−5) = a2 − 2a − 15
2. (b−4)(b−3) = b2 − 7b + 12
3. (c+6)(c−4) = c2 + 2c − 24
4. (d−5)(d+5) = d2 − 25
5. (3e+4)(2e−2)= 6e2 +2e −8

101. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
Different Method- Area Model
(n + 7)(n+3)
n + 7
n
+ 3

102. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
Different Method- Area Model
(n + 7)(n+3)
n + 7
n
+ 3
n2

103. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
Different Method- Area Model
(n + 7)(n+3)
n + 7
n
+ 3
n2 + 7n

104. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
Different Method- Area Model
(n + 7)(n+3)
n + 7
n
+ 3
n2 + 7n
+3n

105. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
Different Method- Area Model
(n + 7)(n+3)
n + 7
n
+ 3
n2 + 7n
+3n +21

106. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
Different Method- Area Model
(n + 7)(n+3)
n + 7
n
+ 3
n2 + 7n
+3n +21

107. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
Different Method- Area Model
(n + 7)(n+3)
n + 7
n
+ 3
n2 + 7n
+3n +21

108. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
Different Method- Area Model
(n + 7)(n+3)
n + 7
n
+ 3
n2 + 7n
+3n +21
n2 + 10n + 21

109. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
(a-5)(a+4)
a -5
a
+ 4

110. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
(a-5)(a+4)
a -5
a
+ 4
a2

111. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
(a-5)(a+4)
a -5
a
+ 4
a2 -5a

112. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
(a-5)(a+4)
a -5
a
+ 4
a2 -5a
+4a

113. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
(a-5)(a+4)
a -5
a
+ 4
a2 -5a
+4a -20

114. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
(a-5)(a+4)
a -5
a
+ 4
a2 -5a
+4a -20

115. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
(a-5)(a+4)
a -5
a
+ 4
a2 -5a
+4a -20

116. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
(a-5)(a+4)
a -5
a
+ 4
a2 -5a
+4a -20
a2 – 1a – 20

117. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
(a – 6)(a + 5)
(b + 4)(b – 8)
(c – 3)(4c + 5)
(3d – 6)(4d + 2)

118. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
(a – 6)(a + 5) = a2 – 1a – 30
(b + 4)(b – 8)
(c – 3)(4c + 5)
(3d – 6)(4d + 2)

119. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
(a – 6)(a + 5) = a2 – 1a – 30
(b + 4)(b – 8) = b2 – 4b – 32
(c – 3)(4c + 5)
(3d – 6)(4d + 2)

120. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
(a – 6)(a + 5) = a2 – 1a – 30
(b + 4)(b – 8) = b2 – 4b – 32
(c – 3)(4c + 5) = 4c2 – 7c – 15
(3d – 6)(4d + 2)

121. 8.A.8- MULTIPLY A BINOMIAL BY A
BINOMIAL
(a – 6)(a + 5) = a2 – 1a – 30
(b + 4)(b – 8) = b2 – 4b – 32
(c – 3)(4c + 5) = 4c2 – 7c – 15
(3d – 6)(4d + 2) = 12d2 – 18d – 12

122. 8.A.7 ADD AND SUBTRACT
POLYNOMIALS
 The main concept is Like Terms: matching
variables (including their exponents)
 LIKE: can be combined! Rules of exponents don’t
come into play because you’re not x/÷. Leave
variables as is!!
ax + 5ax
 NON-LIKE

123. 8.A.7 ADD AND SUBTRACT
POLYNOMIALS
 The main concept is Like Terms: matching
variables (including their exponents)
 LIKE: can be combined! Rules of exponents don’t
come into play because you’re not x/÷. Leave
variables as is!!
ax + 5ax = 6ax
2b2 + 6b2
 NON-LIKE

124. 8.A.7 ADD AND SUBTRACT
POLYNOMIALS
 The main concept is Like Terms: matching
variables (including their exponents)
 LIKE: can be combined! Rules of exponents don’t
come into play because you’re not x/÷. Leave
variables as is!!
ax + 5ax = 6ax
2b2 + 6b2 = 8b2
 NON-LIKE

125. 8.A.7 ADD AND SUBTRACT
POLYNOMIALS
 The main concept is Like Terms: matching
variables (including their exponents)
 LIKE: can be combined! Rules of exponents don’t
come into play because you’re not x/÷. Leave
variables as is!!
ax + 5ax = 6ax
2b2 + 6b2 = 8b2
-3acd − 4acd
 NON-LIKE

126. 8.A.7 ADD AND SUBTRACT
POLYNOMIALS
 The main concept is Like Terms: matching
variables (including their exponents)
 LIKE: can be combined! Rules of exponents don’t
come into play because you’re not x/÷. Leave
variables as is!!
ax + 5ax = 6ax
2b2 + 6b2 = 8b2
-3acd − 4acd = -7acd
 NON-LIKE

127. 8.A.7 ADD AND SUBTRACT
POLYNOMIALS
 The main concept is Like Terms: matching
variables (including their exponents)
 LIKE: can be combined! Rules of exponents don’t
come into play because you’re not x/÷. Leave
variables as is!!
ax + 5ax = 6ax
2b2 + 6b2 = 8b2
-3acd − 4acd = -7acd
 NON-LIKE: can’t be combined!

128. 8.A.7 ADD AND SUBTRACT
POLYNOMIALS
 The main concept is Like Terms: matching variables
(including their exponents)
 LIKE: can be combined! Rules of exponents don’t
come into play because you’re not x/÷. Leave variables
as is!!
ax + 5ax = 6ax
2b2 + 6b2 = 8b2
-3acd − 4acd = -7acd
 NON-LIKE: can’t be combined!
5x – 4y

129. 8.A.7 ADD AND SUBTRACT
POLYNOMIALS
 The main concept is Like Terms: matching variables
(including their exponents)
 LIKE: can be combined! Rules of exponents don’t
come into play because you’re not x/÷. Leave variables
as is!!
ax + 5ax = 6ax
2b2 + 6b2 = 8b2
-3acd − 4acd = -7acd
 NON-LIKE: can’t be combined!
5x – 4y
4a3 + 3a

130. COMBINING LIKE TERMS
 Always simplify to the minimum number of
terms
 Constants can be combined

131. COMBINING LIKE TERMS
 Always simplify to the minimum number of
terms
 Use the sign in front of the term as the operator
 Constants can be combined
 Examples:
1) 5x – 6 + 2x =

132. COMBINING LIKE TERMS
 Always simplify to the minimum number of
terms
 Use the sign in front of the term as the operator
 Constants can be combined
 Examples:
1) 5x – 6 + 2x = 7x – 6

133. COMBINING LIKE TERMS
 Always simplify to the minimum number of
terms
 Use the sign in front of the term as the operator
 Constants can be combined
 Examples:
1) 5x – 6 + 2x = 7x – 6
2) -8 + 4g – 5 + 2g=

134. COMBINING LIKE TERMS
 Always simplify to the minimum number of
terms
 Use the sign in front of the term as the operator
 Constants can be combined
 Examples:
1) 5x – 6 + 2x = 7x – 6
2) -8 + 4g – 5 + 2g= 6g – 13

135. COMBINING LIKE TERMS
 Always simplify to the minimum number of
terms
 Use the sign in front of the term as the operator
 Constants can be combined
 Examples:
1) 5x – 6 + 2x = 7x – 6
2) -8 + 4g – 5 + 2g= 6g – 13
3) 3(5 + m) + 4 – 5m=

136. COMBINING LIKE TERMS
 Always simplify to the minimum number of
terms
 Use the sign in front of the term as the operator
 Constants can be combined
 Examples:
1) 5x – 6 + 2x = 7x – 6
2) -8 + 4g – 5 + 2g= 6g – 13
3) 3(5 + m) + 4 – 5m=
15 + 3m + 4 – 5m =

137. COMBINING LIKE TERMS
 Always simplify to the minimum number of
terms
 Use the sign in front of the term as the operator
 Constants can be combined
 Examples:
1) 5x – 6 + 2x = 7x – 6
2) -8 + 4g – 5 + 2g= 6g – 13
3) 3(5 + m) + 4 – 5m=
15 + 3m + 4 – 5m = 19 – 2m

138. COMBINING LIKE TERMS
 You Try Some:
 1) 5a + 8 – 7a + 2
 2) 3p – 3p + 2
 3) 5h + 4h + 7h – 16h
 4) 7 – 4a + 3a – 10
 5) 4 – 2(b – 4) + 4b

139. COMBINING LIKE TERMS
 You Try Some:
 1) 5a + 8 – 7a + 2 = -2a + 10
 2) 3p – 3p + 2
 3) 5h + 4h + 7h – 16h
 4) 7 – 4a + 3a – 10
 5) 4 – 2(b – 4) + 4b

140. COMBINING LIKE TERMS
 You Try Some:
 1) 5a + 8 – 7a + 2 = -2a + 10
 2) 3p – 3p + 2 = 0p + 2
 3) 5h + 4h + 7h – 16h
 4) 7 – 4a + 3a – 10
 5) 4 – 2(b – 4) + 4b

141. COMBINING LIKE TERMS
 You Try Some:
 1) 5a + 8 – 7a + 2 = -2a + 10
 2) 3p – 3p + 2 = 0p + 2 = 2
 3) 5h + 4h + 7h – 16h
 4) 7 – 4a + 3a – 10
 5) 4 – 2(b – 4) + 4b

142. COMBINING LIKE TERMS
 You Try Some:
 1) 5a + 8 – 7a + 2 = -2a + 10
 2) 3p – 3p + 2 = 0p + 2 = 2
 3) 5h + 4h + 7h – 16h = 0h = 0
 4) 7 – 4a + 3a – 10
 5) 4 – 2(b – 4) + 4b

143. COMBINING LIKE TERMS
 You Try Some:
 1) 5a + 8 – 7a + 2 = -2a + 10
 2) 3p – 3p + 2 = 0p + 2 = 2
 3) 5h + 4h + 7h – 16h = 0h = 0
 4) 7 – 4a + 3a – 10 = -3 – 1a
 5) 4 – 2(b – 4) + 4b

144. COMBINING LIKE TERMS
 You Try Some:
 1) 5a + 8 – 7a + 2 = -2a + 10
 2) 3p – 3p + 2 = 0p + 2 = 2
 3) 5h + 4h + 7h – 16h = 0h = 0
 4) 7 – 4a + 3a – 10 = -3 – 1a
 5) 4 – 2(b – 4) + 4b =
4 – 2b + 8 + 4b =

145. COMBINING LIKE TERMS
 You Try Some:
 1) 5a + 8 – 7a + 2 = -2a + 10
 2) 3p – 3p + 2 = 0p + 2 = 2
 3) 5h + 4h + 7h – 16h = 0h = 0
 4) 7 – 4a + 3a – 10 = -3 – 1a
 5) 4 – 2(b – 4) + 4b =
4 – 2b + 8 + 4b = 12 + 2b

146. 8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
(8a4 + 2a6) + (5a4 + 3a6)
(6b3 + 2b) + (5b − 4b3)

147. 8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
(8a4 + 2a6) + (5a4 + 3a6)
+ 5a4 + 3a6
(6b3 + 2b) + (5b − 4b3)

148. 8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
(8a4 + 2a6) + (5a4 + 3a6)
+ 5a4 + 3a6
(6b3 + 2b) + (5b − 4b3)

149. 8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
(8a4 + 2a6) + (5a4 + 3a6)
+ 5a4 + 3a6
13a4 + 5a6
(6b3 + 2b) + (5b − 4b3)

150. 8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
(8a4 + 2a6) + (5a4 + 3a6)
+ 5a4 + 3a6
13a4 + 5a6 This can’t be simplified further
(6b3 + 2b) + (5b − 4b3)

151. 8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
(8a4 + 2a6) + (5a4 + 3a6)
+ 5a4 + 3a6
13a4 + 5a6 This can’t be simplified further
(6b3 + 2b) + (5b − 4b3)

152. 8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
(8a4 + 2a6) + (5a4 + 3a6)
+ 5a4 + 3a6
13a4 + 5a6 This can’t be simplified further
(6b3 + 2b) + (5b − 4b3)
−4b3 + 5b

153. 8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
(8a4 + 2a6) + (5a4 + 3a6)
+ 5a4 + 3a6
13a4 + 5a6 This can’t be simplified further
(6b3 + 2b) + (5b − 4b3)
−4b3 + 5b It switches to line up like terms

154. 8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
(8a4 + 2a6) + (5a4 + 3a6)
+ 5a4 + 3a6
13a4 + 5a6 This can’t be simplified further
(6b3 + 2b) + (5b − 4b3)
−4b3 + 5b It switches to line up like terms
2b3 + 7b

155. 8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
 (8c5 + 3c) + (-5c5 + 6c2)

156. 8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
 (8c5 + 3c) + (-5c5 + 6c2)

157. 8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
 (8c5 + 3c) + (-5c5 + 6c2)
-5c5 + 6c2

158. 8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
 (8c5 + 3c) + (-5c5 + 6c2)
-5c5 + 6c2

159. 8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
 (8c5 + 3c) + (-5c5 + 6c2)
–5c5 + 6c2

160. 8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
 (8c5 + 3c) + (-5c5 + 6c2)
–5c5 + 6c2
3c5 + 3c + 6c2

161. 8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
 (8c5 + 3c) + (-5c5 + 6c2)
–5c5 + 6c2 So if there’s no like term, leave
3c5 + 3c + 6c2 a gap

162. 8.A.7 ADD POLYNOMIALS
 You Try!
 1. (8a3 + 1a) + (6a + 7a3)
 2. (6x2 + 11yz) + (8x2 – 9yz)
 3. (3b4 – 2b2) + (6b4 + ba + 9b2)

163. 8.A.7 ADD POLYNOMIALS
 You Try!
 1. (8a3 + 1a) + (6a + 7a3)
15a3 + 7a
 2. (6x2 + 11yz) + (8x2 – 9yz)
 3. (3b4 – 2b2) + (6b4 + ba + 9b2)

164. 8.A.7 ADD POLYNOMIALS
 You Try!
 1. (8a3 + 1a) + (6a + 7a3)
15a3 + 7a
 2. (6x2 + 11yz) + (8x2 – 9yz)
14x2 + 2yz
 3. (3b4 – 2b2) + (6b4 + ba + 9b2)

165. 8.A.7 ADD POLYNOMIALS
 You Try!
 1. (8a3 + 1a) + (6a + 7a3)
15a3 + 7a
 2. (6x2 + 11yz) + (8x2 – 9yz)
14x2 + 2yz
 3. (3b4 – 2b2) + (6b4 + ba + 9b2)
9b4 + 7b2 + ba

166. 8.A.7 ADD POLYNOMIALS
 Worksheet!

169. 8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
 (7c4 + 4c) + (5c3 + 2c)
+ 2c + 5c3
7c4 + 6c + 5c3 be careful to line up like terms
only!
 (d3 – 4d2 + 5) + (2d3 +6d2 + 8d)

170. 8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
 (7c4 + 4c) + (5c3 + 2c)
+ 2c + 5c3
7c4 + 6c + 5c3 be careful to line up like terms
only!
 (d3 – 4d2 + 5) + (2d3 +6d2 + 8d)

171. 8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
 (7c4 + 4c) + (5c3 + 2c)
+ 2c + 5c3
7c4 + 6c + 5c3 be careful to line up like terms
only!
 (d3 – 4d2 + 5) + (2d3 +6d2 + 8d)
+2d3 +6d2 +8d)

172. 8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
 (7c4 + 4c) + (5c3 + 2c)
+ 2c + 5c3
7c4 + 6c + 5c3 be careful to line up like
terms only!
 (d3 – 4d2 + 5) + (2d3 +6d2 + 8d)
+2d3 +6d2 +8d)
3d3 + 2d2 +5 + 8d

173. 8.A.7 ADD POLYNOMIALS
 You Try!
1. (4x2y + 3y) + (8x2y +9y)
2. (5a3 + 10a) + (-4a3 + 6a)
3. (2b4 – 7b2) + (5b4 + 12ba + 9b2)

174. 8.A.7 SUBTRACT POLYNOMIALS
 (8a2b + 5a) – (5a2b + 2a)
Remember! K C C
The operator changes to addition and then all the signs of the
terms on the inside change !
(8a2b + 5a) – (5a2b + 2a)

175. 8.A.7 SUBTRACT POLYNOMIALS
 (8a2b + 5a) – (5a2b + 2a)
Remember! K C C
The operator changes to addition and then all the signs of the
terms on the inside change !
(8a2b + 5a) – (5a2b + 2a)
+

176. 8.A.7 SUBTRACT POLYNOMIALS
 (8a2b + 5a) – (5a2b + 2a)
Remember! K C C
The operator changes to addition and then all the signs of the
terms on the inside change !
(8a2b + 5a) – (5a2b + 2a)
+ (-5a2b

177. 8.A.7 SUBTRACT POLYNOMIALS
 (8a2b + 5a) – (5a2b + 2a)
Remember! K C C
The operator changes to addition and then all the signs of the
terms on the inside change !
(8a2b + 5a) – (5a2b + 2a)
+ (-5a2b – 2a)

178. 8.A.7 SUBTRACT POLYNOMIALS
 (8a2b + 5a) – (5a2b + 2a)
Remember! K C C
The operator changes to addition and then all the signs of the
terms on the inside change !
(8a2b + 5a) – (5a2b + 2a)
+ (-5a2b – 2a)

179. 8.A.7 SUBTRACT POLYNOMIALS
 (8a2b + 5a) – (5a2b + 2a)
Remember! K C C
The operator changes to addition and then all the signs of the
terms on the inside change !
(8a2b + 5a) – (5a2b + 2a)
+ (-5a2b – 2a)

180. 8.A.7 SUBTRACT POLYNOMIALS
 (8a2b + 5a) – (5a2b + 2a)
Remember! K C C
The operator changes to addition and then all the signs of the
terms on the inside change !
(8a2b + 5a) – (5a2b + 2a)
+ (-5a2b – 2a)
+ (-5a2b – 2a)

181. 8.A.7 SUBTRACT POLYNOMIALS
 (8a2b + 5a) – (5a2b + 2a)
Remember! K C C
The operator changes to addition and then all the signs of the
terms on the inside change !
(8a2b + 5a) – (5a2b + 2a)
+ (-5a2b – 2a)
+ (-5a2b – 2a)
3a2b

182. 8.A.7 SUBTRACT POLYNOMIALS
 (8a2b + 5a) – (5a2b + 2a)
Remember! K C C
The operator changes to addition and then all the signs of the
terms on the inside change !
(8a2b + 5a) – (5a2b + 2a)
+ (-5a2b – 2a)
+ (-5a2b – 2a)
3a2b + 3a

183. 8.A.7 SUBTRACT POLYNOMIALS
 Another example!
(6b3 – 8bc) – (8b3 + 9bc)

184. 8.A.7 SUBTRACT POLYNOMIALS
 Another example!
(6b3 – 8bc) – (8b3 + 9bc)
K C C

185. 8.A.7 SUBTRACT POLYNOMIALS
 Another example!
(6b3 – 8bc) – (8b3 + 9bc)
K C C
+

186. 8.A.7 SUBTRACT POLYNOMIALS
 Another example!
(6b3 – 8bc) – (8b3 + 9bc)
K C C
+ (-8b3

187. 8.A.7 SUBTRACT POLYNOMIALS
 Another example!
(6b3 – 8bc) – (8b3 + 9bc)
K C C
+ (-8b3 – 9bc)

188. 8.A.7 SUBTRACT POLYNOMIALS
 Another example!
(6b3 – 8bc) – (8b3 + 9bc)
K C C
+ (-8b3 – 9bc)

189. 8.A.7 SUBTRACT POLYNOMIALS
 Another example!
(6b3 – 8bc) – (8b3 + 9bc)
K C C
+ (-8b3 – 9bc)

190. 8.A.7 SUBTRACT POLYNOMIALS
 Another example!
(6b3 – 8bc) – (8b3 + 9bc)
K C C
+ (-8b3 – 9bc)
+ (-8b3 – 9bc)

191. 8.A.7 SUBTRACT POLYNOMIALS
 Another example!
(6b3 – 8bc) – (8b3 + 9bc)
K C C
+ (-8b3 – 9bc)
+ (-8b3 – 9bc)
-2b3

192. 8.A.7 SUBTRACT POLYNOMIALS
 Another example!
(6b3 – 8bc) – (8b3 + 9bc)
K C C
+ (-8b3 – 9bc)
+ (-8b3 – 9bc)
-2b3 – 17bc

193. 8.A.7 SUBTRACT POLYNOMIALS
 (15c3m – 4c2 + 8m) – (9c3m – 10m)

194. 8.A.7 SUBTRACT POLYNOMIALS
 (15c3m – 4c2 + 8m) – (9c3m – 10m)
K C C
+ (-9c3m +10m)

195. 8.A.7 SUBTRACT POLYNOMIALS
 (15c3m – 4c2 + 8m) – (9c3m – 10m)
K C C
+ (-9c3m +10m)

196. 8.A.7 SUBTRACT POLYNOMIALS
 (15c3m – 4c2 + 8m) – (9c3m – 10m)
K C C
+ (-9c3m +10m)

197. 8.A.7 SUBTRACT POLYNOMIALS
 (15c3m – 4c2 + 8m) – (9c3m – 10m)
K C C
+ (-9c3m +10m)
+ (-9c3m +10m) Remember to line up like terms!
6c3m – 4c2 + 18m

198. 8.A.7 SUBTRACT POLYNOMIALS
 You Try… On your own!
(-5c3 – 4c4) – (2c3 + 5c4)
(5a3 + 7b) – (6b – 4a3)
(20v2 – 5m) – (12v2 – 4m + 2)
(8g4 + 6a – 7) – (5g4 – 10)
(9a2 – 5m) – (-6a2 + 8m)

199. 8.A.7 SUBTRACT POLYNOMIALS
 You Try… On your own!
(-5c3 – 4c4) – (2c3 + 5c4)
-7c3 – 9c4
(5a3 + 7b) – (6b – 4a3)
(20v2 – 5m) – (12v2 – 4m + 2)
(8g4 + 6a – 7) – (5g4 – 10)
(9a2 – 5m) – (-6a2 + 8m)

200. 8.A.7 SUBTRACT POLYNOMIALS
 You Try… On your own!
(-5c3 – 4c4) – (2c3 + 5c4)
-7c3 – 9c4
(5a3 + 7b) – (6b – 4a3)
9a3 + b
(20v2 – 5m) – (12v2 – 4m + 2)
(8g4 + 6a – 7) – (5g4 – 10)
(9a2 – 5m) – (-6a2 + 8m)

201. 8.A.7 SUBTRACT POLYNOMIALS
 You Try… On your own!
(-5c3 – 4c4) – (2c3 + 5c4)
-7c3 – 9c4
(5a3 + 7b) – (6b – 4a3)
9a3 + b
(20v2 – 5m) – (12v2 – 4m + 2)
8v2 – m – 2
(8g4 + 6a – 7) – (5g4 – 10)
(9a2 – 5m) – (-6a2 + 8m)

202. 8.A.7 SUBTRACT POLYNOMIALS
 You Try… On your own!
(-5c3 – 4c4) – (2c3 + 5c4)
-7c3 – 9c4
(5a3 + 7b) – (6b – 4a3)
9a3 + b
(20v2 – 5m) – (12v2 – 4m + 2)
8v2 – m – 2
(8g4 + 6a – 7) – (5g4 – 10)
3g3 + 6a + 3
(9a2 – 5m) – (-6a2 + 8m)

203. 8.A.7 SUBTRACT POLYNOMIALS
 You Try… On your own!
(-5c3 – 4c4) – (2c3 + 5c4)
-7c3 – 9c4
(5a3 + 7b) – (6b – 4a3)
9a3 + b
(20v2 – 5m) – (12v2 – 4m + 2)
8v2 – m – 2
(8g4 + 6a – 7) – (5g4 – 10)
3g3 + 6a + 3
(9a2 – 5m) – (-6a2 + 8m)
15a2 – 13m

204. 8.A.7 ADD AND SUBTRACT
POLYNOMIALS
 1. (4a – 6a3) + (8a3 – 3a)
 2. (7g + 2g2) – (7g2 + 2g)
 3. (3m2 – 2m + 6) – (3m – 2m2)
 4. (5c2 + 3c3) + (4c3 + 1)
 5. (7x2 + 4) – (5 + 9x2)
 6. (6n2 – 3n3) – (4n3 – 2n2 + 4n2)

205. 8.A.7 ADD AND SUBTRACT
POLYNOMIALS
 1. (4a – 6a3) + (8a3 – 3a) = a + 2a3
 2. (7g + 2g2) – (7g2 + 2g)
 3. (3m2 – 2m + 6) – (3m – 2m2)
 4. (5c2 + 3c3) + (4c3 + 1)
 5. (7x2 + 4) – (5 + 9x2)
 6. (6n2 – 3n3) – (4n3 – 2n2 + 4n2)

206. 8.A.7 ADD AND SUBTRACT
POLYNOMIALS
 1. (4a – 6a3) + (8a3 – 3a) = a + 2a3
 2. (7g + 2g2) – (7g2 + 2g) = 5g – 5g2
 3. (3m2 – 2m + 6) – (3m – 2m2)
 4. (5c2 + 3c3) + (4c3 + 1)
 5. (7x2 + 4) – (5 + 9x2)
 6. (6n2 – 3n3) – (4n3 – 2n2 + 4n2)

207. 8.A.7 ADD AND SUBTRACT
POLYNOMIALS
 1. (4a – 6a3) + (8a3 – 3a) = a + 2a3
 2. (7g + 2g2) – (7g2 + 2g) = 5g – 5g2
 3. (3m2 – 2m + 6) – (3m – 2m2) = 5m2 – 5m + 6
 4. (5c2 + 3c3) + (4c3 + 1)
 5. (7x2 + 4) – (5 + 9x2)
 6. (6n2 – 3n3) – (4n3 – 2n2 + 4n2)

208. 8.A.7 ADD AND SUBTRACT
POLYNOMIALS
 1. (4a – 6a3) + (8a3 – 3a) = a + 2a3
 2. (7g + 2g2) – (7g2 + 2g) = 5g – 5g2
 3. (3m2 – 2m + 6) – (3m – 2m2) = 5m2 – 5m + 6
 4. (5c2 + 3c3) + (4c3 + 1) = 7c3 + 5c2 + 1
 5. (7x2 + 4) – (5 + 9x2)
 6. (6n2 – 3n3) – (4n3 – 2n2 + 4n2)

209. 8.A.7 ADD AND SUBTRACT
POLYNOMIALS
 1. (4a – 6a3) + (8a3 – 3a) = a + 2a3
 2. (7g + 2g2) – (7g2 + 2g) = 5g – 5g2
 3. (3m2 – 2m + 6) – (3m – 2m2) = 5m2 – 5m + 6
 4. (5c2 + 3c3) + (4c3 + 1) = 7c3 + 5c2 + 1
 5. (7x2 + 4) – (5 + 9x2) = 2x2 – 1
 6. (6n2 – 3n3) – (4n3 – 2n2 + 4n2)

210. 8.A.7 ADD AND SUBTRACT
POLYNOMIALS
 1. (4a – 6a3) + (8a3 – 3a) = a + 2a3
 2. (7g + 2g2) – (7g2 + 2g) = 5g – 5g2
 3. (3m2 – 2m + 6) – (3m – 2m2) = 5m2 – 5m + 6
 4. (5c2 + 3c3) + (4c3 + 1) = 7c3 + 5c2 + 1
 5. (7x2 + 4) – (5 + 9x2) = 2x2 – 1
 6. (6n2 – 3n3) – (4n3 – 2n2 + 4n2) = 4n2 – 7n3