1. Multiplication Formulas

2. Multiplication Formulas
There are some important patterns in multiplying expressions
that it is worthwhile to memorize.

3. Multiplication Formulas
There are some important patterns in multiplying expressions
that it is worthwhile to memorize.
The two binomials (A + B) and (A – B) are said to be the
conjugate of each other.

4. Multiplication Formulas
There are some important patterns in multiplying expressions
that it is worthwhile to memorize.
The two binomials (A + B) and (A – B) are said to be the
conjugate of each other.
For example, the conjugate of (3x + 2) is (3x – 2),

5. Multiplication Formulas
There are some important patterns in multiplying expressions
that it is worthwhile to memorize.
The two binomials (A + B) and (A – B) are said to be the
conjugate of each other.
For example, the conjugate of (3x + 2) is (3x – 2), and
the conjugate of (2ab – c) is (2ab + c).

6. Multiplication Formulas
There are some important patterns in multiplying expressions
that it is worthwhile to memorize.
The two binomials (A + B) and (A – B) are said to be the
conjugate of each other.
For example, the conjugate of (3x + 2) is (3x – 2), and
the conjugate of (2ab – c) is (2ab + c).
Note: The conjugate is different from the opposite.
The opposite of (3x + 2) is (–3x – 2).

7. Multiplication Formulas
There are some important patterns in multiplying expressions
that it is worthwhile to memorize.
The two binomials (A + B) and (A – B) are said to be the
conjugate of each other.
For example, the conjugate of (3x + 2) is (3x – 2), and
the conjugate of (2ab – c) is (2ab + c).
Note: The conjugate is different from the opposite.
The opposite of (3x + 2) is (–3x – 2).
I. Difference of Squares Formula

8. Multiplication Formulas
There are some important patterns in multiplying expressions
that it is worthwhile to memorize.
The two binomials (A + B) and (A – B) are said to be the
conjugate of each other.
For example, the conjugate of (3x + 2) is (3x – 2), and
the conjugate of (2ab – c) is (2ab + c).
Note: The conjugate is different from the opposite.
The opposite of (3x + 2) is (–3x – 2).
I. Difference of Squares Formula
(A + B)(A – B)
Conjugate Product

9. Multiplication Formulas
There are some important patterns in multiplying expressions
that it is worthwhile to memorize.
The two binomials (A + B) and (A – B) are said to be the
conjugate of each other.
For example, the conjugate of (3x + 2) is (3x – 2), and
the conjugate of (2ab – c) is (2ab + c).
Note: The conjugate is different from the opposite.
The opposite of (3x + 2) is (–3x – 2).
I. Difference of Squares Formula
(A + B)(A – B) = A2 – B2
Conjugate Product Difference of Squares

10. There are some important patterns in multiplying expressions
that it is worthwhile to memorize.
The two binomials (A + B) and (A – B) are said to be the
conjugate of each other.
I. Difference of Squares Formula
(A + B)(A – B) = A2 – B2
Conjugate Product Difference of Squares
To verify this :
(A + B)(A – B)
Multiplication Formulas
For example, the conjugate of (3x + 2) is (3x – 2), and
the conjugate of (2ab – c) is (2ab + c).
Note: The conjugate is different from the opposite.
The opposite of (3x + 2) is (–3x – 2).

11. Multiplication Formulas
There are some important patterns in multiplying expressions
that it is worthwhile to memorize.
The two binomials (A + B) and (A – B) are said to be the
conjugate of each other.
For example, the conjugate of (3x + 2) is (3x – 2), and
the conjugate of (2ab – c) is (2ab + c).
Note: The conjugate is different from the opposite.
The opposite of (3x + 2) is (–3x – 2).
I. Difference of Squares Formula
(A + B)(A – B) = A2 – B2
Conjugate Product Difference of Squares
To verify this :
(A + B)(A – B) = A2 – AB + AB – B2

12. Multiplication Formulas
There are some important patterns in multiplying expressions
that it is worthwhile to memorize.
The two binomials (A + B) and (A – B) are said to be the
conjugate of each other.
For example, the conjugate of (3x + 2) is (3x – 2), and
the conjugate of (2ab – c) is (2ab + c).
Note: The conjugate is different from the opposite.
The opposite of (3x + 2) is (–3x – 2).
I. Difference of Squares Formula
(A + B)(A – B) = A2 – B2
Conjugate Product Difference of Squares
To verify this :
(A + B)(A – B) = A2 – AB + AB – B2
= A2 – B2

13. Multiplication Formulas
Here are some examples of squaring:

14. Multiplication Formulas
Here are some examples of squaring: (3x)2 =

15. Multiplication Formulas
Here are some examples of squaring: (3x)2 = 9x2,

16. Multiplication Formulas
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 =

17. Multiplication Formulas
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2,

18. Multiplication Formulas
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2

19. Multiplication Formulas
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.

20. Multiplication Formulas
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
Example A. Expand.
a. (3x + 2)(3x – 2)

21. Multiplication Formulas
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
Example A. Expand.
a. (3x + 2)(3x – 2)
(A + B)(A – B)

22. Multiplication Formulas
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
Example A. Expand.
a. (3x + 2)(3x – 2) = (3x)2 – (2)2
(A + B)(A – B) = A2 – B2

23. Multiplication Formulas
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
Example A. Expand.
a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4
(A + B)(A – B) = A2 – B2

24. Multiplication Formulas
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
Example A. Expand.
a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4
(A + B)(A – B) = A2 – B2
b. (2xy – 5z2)(2xy + 5z2)

25. Multiplication Formulas
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
Example A. Expand.
a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4
(A + B)(A – B) = A2 – B2
b. (2xy – 5z2)(2xy + 5z2)
= (2xy)2 – (5z2)2

26. Multiplication Formulas
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
Example A. Expand.
a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4
(A + B)(A – B) = A2 – B2
b. (2xy – 5z2)(2xy + 5z2)
= (2xy)2 – (5z2)2
= 4x2y2 – 25z4

27. Multiplication Formulas
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
Example A. Expand.
a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4
(A + B)(A – B) = A2 – B2
b. (2xy – 5z2)(2xy + 5z2)
= (2xy)2 – (5z2)2
= 4x2y2 – 25z4
II. Square Formulas

28. Multiplication Formulas
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
Example A. Expand.
a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4
(A + B)(A – B) = A2 – B2
b. (2xy – 5z2)(2xy + 5z2)
= (2xy)2 – (5z2)2
= 4x2y2 – 25z4
II. Square Formulas
(A + B)2 = A2 + 2AB + B2

29. Multiplication Formulas
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
Example A. Expand.
a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4
(A + B)(A – B) = A2 – B2
b. (2xy – 5z2)(2xy + 5z2)
= (2xy)2 – (5z2)2
= 4x2y2 – 25z4
II. Square Formulas
(A + B)2 = A2 + 2AB + B2
(A – B)2 = A2 – 2AB + B2

30. Multiplication Formulas
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
Example A. Expand.
a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4
(A + B)(A – B) = A2 – B2
b. (2xy – 5z2)(2xy + 5z2)
= (2xy)2 – (5z2)2
= 4x2y2 – 25z4
II. Square Formulas
(A + B)2 = A2 + 2AB + B2
(A – B)2 = A2 – 2AB + B2
We may check this easily by multiplying,

31. Multiplication Formulas
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
Example A. Expand.
a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4
(A + B)(A – B) = A2 – B2
b. (2xy – 5z2)(2xy + 5z2)
= (2xy)2 – (5z2)2
= 4x2y2 – 25z4
II. Square Formulas
(A + B)2 = A2 + 2AB + B2
(A – B)2 = A2 – 2AB + B2
We may check this easily by multiplying,
(A + B)2 = (A + B)(A + B)

32. Multiplication Formulas
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
Example A. Expand.
a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4
(A + B)(A – B) = A2 – B2
b. (2xy – 5z2)(2xy + 5z2)
= (2xy)2 – (5z2)2
= 4x2y2 – 25z4
II. Square Formulas
(A + B)2 = A2 + 2AB + B2
(A – B)2 = A2 – 2AB + B2
We may check this easily by multiplying,
(A + B)2 = (A + B)(A + B) = A2 + AB + BA + B2

33. Multiplication Formulas
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
Example A. Expand.
a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4
(A + B)(A – B) = A2 – B2
b. (2xy – 5z2)(2xy + 5z2)
= (2xy)2 – (5z2)2
= 4x2y2 – 25z4
II. Square Formulas
(A + B)2 = A2 + 2AB + B2
(A – B)2 = A2 – 2AB + B2
We may check this easily by multiplying,
(A + B)2 = (A + B)(A + B) = A2 + AB + BA + B2 = A2 + 2AB + B2

34. Multiplication Formulas
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
Example A. Expand.
a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4
(A + B)(A – B) = A2 – B2
b. (2xy – 5z2)(2xy + 5z2)
= (2xy)2 – (5z2)2
= 4x2y2 – 25z4
II. Square Formulas
(A + B)2 = A2 + 2AB + B2
(A – B)2 = A2 – 2AB + B2
We may check this easily by multiplying,
(A + B)2 = (A + B)(A + B) = A2 + AB + BA + B2 = A2 + 2AB + B2
We say that “(A + B)2 is A2, B2, plus twice A*B”,

35. Multiplication Formulas
Here are some examples of squaring: (3x)2 = 9x2,
(2xy)2 = 4x2y2, and (5z2)2 = 25z4.
Example A. Expand.
a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4
(A + B)(A – B) = A2 – B2
b. (2xy – 5z2)(2xy + 5z2)
= (2xy)2 – (5z2)2
= 4x2y2 – 25z4
II. Square Formulas
(A + B)2 = A2 + 2AB + B2
(A – B)2 = A2 – 2AB + B2
We may check this easily by multiplying,
(A + B)2 = (A + B)(A + B) = A2 + AB + BA + B2 = A2 + 2AB + B2
We say that “(A + B)2 is A2, B2, plus twice A*B”,
and “(A – B)2 is A2, B2, minus twice A*B”.

36. Example B.
a. (3x + 4)2
Multiplication Formulas

37. Example B.
a. (3x + 4)2
(A + B)2
Multiplication Formulas

38. Example B.
a. (3x + 4)2
Multiplication Formulas
(A + B)2 = A2 + 2AB + B2

39. Multiplication Formulas
Example B.
a. (3x + 4)2 = (3x)2
(A + B)2 = A2 + 2AB + B2

40. Multiplication Formulas
Example B.
a. (3x + 4)2 = (3x)2 + 2(3x)(4)
(A + B)2 = A2 + 2AB + B2

41. Multiplication Formulas
Example B.
a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42
(A + B)2 = A2 + 2AB + B2

42. Multiplication Formulas
Example B.
a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16
(A + B)2 = A2 + 2AB + B2

43. Multiplication Formulas
Example B.
a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16
(A + B)2 = A2 + 2AB + B2
b. (3a – 5b)2

44. Multiplication Formulas
Example B.
a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16
(A + B)2 = A2 + 2AB + B2
b. (3a – 5b)2 = (3a)2 – 2(3a)(5b) + (5b)2

45. Multiplication Formulas
Example B.
a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16
(A + B)2 = A2 + 2AB + B2
b. (3a – 5b)2 = (3a)2 – 2(3a)(5b) + (5b)2
= 9a2 – 30ab + 25b2

46. Multiplication Formulas
Example B.
a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16
(A + B)2 = A2 + 2AB + B2
b. (3a – 5b)2 = (3a)2 – 2(3a)(5b) + (5b)2
= 9a2 – 30ab + 25b2
III. Some Applications of the Formulas

47. Multiplication Formulas
Example B.
a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16
(A + B)2 = A2 + 2AB + B2
b. (3a – 5b)2 = (3a)2 – 2(3a)(5b) + (5b)2
= 9a2 – 30ab + 25b2
III. Some Applications of the Formulas
We can use the above formulas to help us multiply.

48. Multiplication Formulas
Example B.
a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16
(A + B)2 = A2 + 2AB + B2
b. (3a – 5b)2 = (3a)2 – 2(3a)(5b) + (5b)2
= 9a2 – 30ab + 25b2
III. Some Applications of the Formulas
We can use the above formulas to help us multiply.
Example C. Calculate. Use the conjugate formula.
a. 51*49

49. Multiplication Formulas
Example B.
a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16
(A + B)2 = A2 + 2AB + B2
b. (3a – 5b)2 = (3a)2 – 2(3a)(5b) + (5b)2
= 9a2 – 30ab + 25b2
III. Some Applications of the Formulas
We can use the above formulas to help us multiply.
Example C. Calculate. Use the conjugate formula.
a. 51*49 = (50 + 1)(50 – 1)

50. Multiplication Formulas
Example B.
a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16
(A + B)2 = A2 + 2AB + B2
b. (3a – 5b)2 = (3a)2 – 2(3a)(5b) + (5b)2
= 9a2 – 30ab + 25b2
III. Some Applications of the Formulas
We can use the above formulas to help us multiply.
Example C. Calculate. Use the conjugate formula.
a. 51*49 = (50 + 1)(50 – 1) = 502 – 12

51. Multiplication Formulas
Example B.
a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16
(A + B)2 = A2 + 2AB + B2
b. (3a – 5b)2 = (3a)2 – 2(3a)(5b) + (5b)2
= 9a2 – 30ab + 25b2
III. Some Applications of the Formulas
We can use the above formulas to help us multiply.
Example C. Calculate. Use the conjugate formula.
a. 51*49 = (50 + 1)(50 – 1) = 502 – 12 = 2,500 – 1 = 2,499

52. Multiplication Formulas
Example B.
a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16
(A + B)2 = A2 + 2AB + B2
b. (3a – 5b)2 = (3a)2 – 2(3a)(5b) + (5b)2
= 9a2 – 30ab + 25b2
III. Some Applications of the Formulas
We can use the above formulas to help us multiply.
Example C. Calculate. Use the conjugate formula.
a. 51*49 = (50 + 1)(50 – 1) = 502 – 12 = 2,500 – 1 = 2,499
b. 52*48

53. Multiplication Formulas
Example B.
a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16
(A + B)2 = A2 + 2AB + B2
b. (3a – 5b)2 = (3a)2 – 2(3a)(5b) + (5b)2
= 9a2 – 30ab + 25b2
III. Some Applications of the Formulas
We can use the above formulas to help us multiply.
Example C. Calculate. Use the conjugate formula.
a. 51*49 = (50 + 1)(50 – 1) = 502 – 12 = 2,500 – 1 = 2,499
b. 52*48 = (50 + 2)(50 – 2) = 502 – 22

54. Multiplication Formulas
Example B.
a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16
(A + B)2 = A2 + 2AB + B2
b. (3a – 5b)2 = (3a)2 – 2(3a)(5b) + (5b)2
= 9a2 – 30ab + 25b2
III. Some Applications of the Formulas
We can use the above formulas to help us multiply.
Example C. Calculate. Use the conjugate formula.
a. 51*49 = (50 + 1)(50 – 1) = 502 – 12 = 2,500 – 1 = 2,499
b. 52*48 = (50 + 2)(50 – 2) = 502 – 22 = 2,500 – 4 = 2,496

55. Multiplication Formulas
Example B.
a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16
(A + B)2 = A2 + 2AB + B2
b. (3a – 5b)2 = (3a)2 – 2(3a)(5b) + (5b)2
= 9a2 – 30ab + 25b2
III. Some Applications of the Formulas
We can use the above formulas to help us multiply.
Example C. Calculate. Use the conjugate formula.
a. 51*49 = (50 + 1)(50 – 1) = 502 – 12 = 2,500 – 1 = 2,499
b. 52*48 = (50 + 2)(50 – 2) = 502 – 22 = 2,500 – 4 = 2,496
c. 63*57 =

56. Multiplication Formulas
Example B.
a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16
(A + B)2 = A2 + 2AB + B2
b. (3a – 5b)2 = (3a)2 – 2(3a)(5b) + (5b)2
= 9a2 – 30ab + 25b2
III. Some Applications of the Formulas
We can use the above formulas to help us multiply.
Example C. Calculate. Use the conjugate formula.
a. 51*49 = (50 + 1)(50 – 1) = 502 – 12 = 2,500 – 1 = 2,499
b. 52*48 = (50 + 2)(50 – 2) = 502 – 22 = 2,500 – 4 = 2,496
c. 63*57 = (60 + 3)(60 – 3) = 602 – 32

57. Multiplication Formulas
Example B.
a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16
(A + B)2 = A2 + 2AB + B2
b. (3a – 5b)2 = (3a)2 – 2(3a)(5b) + (5b)2
= 9a2 – 30ab + 25b2
III. Some Applications of the Formulas
We can use the above formulas to help us multiply.
Example C. Calculate. Use the conjugate formula.
a. 51*49 = (50 + 1)(50 – 1) = 502 – 12 = 2,500 – 1 = 2,499
b. 52*48 = (50 + 2)(50 – 2) = 502 – 22 = 2,500 – 4 = 2,496
c. 63*57 = (60 + 3)(60 – 3) = 602 – 32 = 3,600 – 9 = 3,591

58. Multiplication Formulas
Example B.
a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16
(A + B)2 = A2 + 2AB + B2
b. (3a – 5b)2 = (3a)2 – 2(3a)(5b) + (5b)2
= 9a2 – 30ab + 25b2
III. Some Applications of the Formulas
We can use the above formulas to help us multiply.
Example C. Calculate. Use the conjugate formula.
a. 51*49 = (50 + 1)(50 – 1) = 502 – 12 = 2,500 – 1 = 2,499
b. 52*48 = (50 + 2)(50 – 2) = 502 – 22 = 2,500 – 4 = 2,496
c. 63*57 = (60 + 3)(60 – 3) = 602 – 32 = 3,600 – 9 = 3,591
The conjugate formula
(A + B)(A – B) = A2 – B2
may be used to multiply two numbers of the forms
(A + B) and (A – B) where A2 and B2 can be calculated easily.

59. Multiplication Formulas
The Squaring Formulas.
“(A + B)2 is A2, B2, plus twice A*B”,
“(A – B)2 is A2, B2, minus twice A*B”.

60. Multiplication Formulas
The Squaring Formulas.
“(A + B)2 is A2, B2, plus twice A*B”,
“(A – B)2 is A2, B2, minus twice A*B”.
Example D. Calculate. Use the squaring formulas.
a. 512

61. Multiplication Formulas
The Squaring Formulas.
“(A + B)2 is A2, B2, plus twice A*B”,
“(A – B)2 is A2, B2, minus twice A*B”.
Example D. Calculate. Use the squaring formulas.
a. 512 = (50 + 1)2

62. Multiplication Formulas
The Squaring Formulas.
“(A + B)2 is A2, B2, plus twice A*B”,
“(A – B)2 is A2, B2, minus twice A*B”.
Example D. Calculate. Use the squaring formulas.
a. 512 = (50 + 1)2 = 502 + 12

63. Multiplication Formulas
The Squaring Formulas.
“(A + B)2 is A2, B2, plus twice A*B”,
“(A – B)2 is A2, B2, minus twice A*B”.
Example D. Calculate. Use the squaring formulas.
a. 512 = (50 + 1)2 = 502 + 12 + 2(50)(1)

64. Multiplication Formulas
The Squaring Formulas.
“(A + B)2 is A2, B2, plus twice A*B”,
“(A – B)2 is A2, B2, minus twice A*B”.
Example D. Calculate. Use the squaring formulas.
a. 512 = (50 + 1)2 = 502 + 12 + 2(50)(1)
= 2,500 + 1 + 100

65. Multiplication Formulas
The Squaring Formulas.
“(A + B)2 is A2, B2, plus twice A*B”,
“(A – B)2 is A2, B2, minus twice A*B”.
Example D. Calculate. Use the squaring formulas.
a. 512 = (50 + 1)2 = 502 + 12 + 2(50)(1)
= 2,500 + 1 + 100
= 2,601

66. Multiplication Formulas
The Squaring Formulas.
“(A + B)2 is A2, B2, plus twice A*B”,
“(A – B)2 is A2, B2, minus twice A*B”.
Example D. Calculate. Use the squaring formulas.
a. 512 = (50 + 1)2 = 502 + 12 + 2(50)(1)
= 2,500 + 1 + 100
= 2,601
b. 492

67. Multiplication Formulas
The Squaring Formulas.
“(A + B)2 is A2, B2, plus twice A*B”,
“(A – B)2 is A2, B2, minus twice A*B”.
Example D. Calculate. Use the squaring formulas.
a. 512 = (50 + 1)2 = 502 + 12 + 2(50)(1)
= 2,500 + 1 + 100
= 2,601
b. 492 = (50 – 1)2

68. Multiplication Formulas
The Squaring Formulas.
“(A + B)2 is A2, B2, plus twice A*B”,
“(A – B)2 is A2, B2, minus twice A*B”.
Example D. Calculate. Use the squaring formulas.
a. 512 = (50 + 1)2 = 502 + 12 + 2(50)(1)
= 2,500 + 1 + 100
= 2,601
b. 492 = (50 – 1)2 = 502 + 12

69. Multiplication Formulas
The Squaring Formulas.
“(A + B)2 is A2, B2, plus twice A*B”,
“(A – B)2 is A2, B2, minus twice A*B”.
Example D. Calculate. Use the squaring formulas.
a. 512 = (50 + 1)2 = 502 + 12 + 2(50)(1)
= 2,500 + 1 + 100
= 2,601
b. 492 = (50 – 1)2 = 502 + 12 – 2(50)(1)

70. Multiplication Formulas
The Squaring Formulas.
“(A + B)2 is A2, B2, plus twice A*B”,
“(A – B)2 is A2, B2, minus twice A*B”.
Example D. Calculate. Use the squaring formulas.
a. 512 = (50 + 1)2 = 502 + 12 + 2(50)(1)
= 2,500 + 1 + 100
= 2,601
b. 492 = (50 – 1)2 = 502 + 12 – 2(50)(1)
= 2,500 + 1 – 100

71. Multiplication Formulas
The Squaring Formulas.
“(A + B)2 is A2, B2, plus twice A*B”,
“(A – B)2 is A2, B2, minus twice A*B”.
Example D. Calculate. Use the squaring formulas.
a. 512 = (50 + 1)2 = 502 + 12 + 2(50)(1)
= 2,500 + 1 + 100
= 2,601
b. 492 = (50 – 1)2 = 502 + 12 – 2(50)(1)
= 2,500 + 1 – 100
= 2,401

72. Multiplication Formulas
The Squaring Formulas.
“(A + B)2 is A2, B2, plus twice A*B”,
“(A – B)2 is A2, B2, minus twice A*B”.
Example D. Calculate. Use the squaring formulas.
a. 512 = (50 + 1)2 = 502 + 12 + 2(50)(1)
= 2,500 + 1 + 100
= 2,601
b. 492 = (50 – 1)2 = 502 + 12 – 2(50)(1)
= 2,500 + 1 – 100
= 2,401
b. (50½) 2 = (50 + ½ )2

73. Multiplication Formulas
The Squaring Formulas.
“(A + B)2 is A2, B2, plus twice A*B”,
“(A – B)2 is A2, B2, minus twice A*B”.
Example D. Calculate. Use the squaring formulas.
a. 512 = (50 + 1)2 = 502 + 12 + 2(50)(1)
= 2,500 + 1 + 100
= 2,601
b. 492 = (50 – 1)2 = 502 + 12 – 2(50)(1)
= 2,500 + 1 – 100
= 2,401
b. (50½) 2 = (50 + ½ )2 = 502 + ½ 2

74. Multiplication Formulas
The Squaring Formulas.
“(A + B)2 is A2, B2, plus twice A*B”,
“(A – B)2 is A2, B2, minus twice A*B”.
Example D. Calculate. Use the squaring formulas.
a. 512 = (50 + 1)2 = 502 + 12 + 2(50)(1)
= 2,500 + 1 + 100
= 2,601
b. 492 = (50 – 1)2 = 502 + 12 – 2(50)(1)
= 2,500 + 1 – 100
= 2,401
b. (50½) 2 = (50 + ½ )2 = 502 + ½ 2 + 2 (½) (50)

75. Multiplication Formulas
The Squaring Formulas.
“(A + B)2 is A2, B2, plus twice A*B”,
“(A – B)2 is A2, B2, minus twice A*B”.
Example D. Calculate. Use the squaring formulas.
a. 512 = (50 + 1)2 = 502 + 12 + 2(50)(1)
= 2,500 + 1 + 100
= 2,601
b. 492 = (50 – 1)2 = 502 + 12 – 2(50)(1)
= 2,500 + 1 – 100
= 2,401
b. (50½) 2 = (50 + ½ )2 = 502 + ½ 2 + 2 (½) (50)
= 2,500 + 1/4 + 50

76. Multiplication Formulas
The Squaring Formulas.
“(A + B)2 is A2, B2, plus twice A*B”,
“(A – B)2 is A2, B2, minus twice A*B”.
Example D. Calculate. Use the squaring formulas.
a. 512 = (50 + 1)2 = 502 + 12 + 2(50)(1)
= 2,500 + 1 + 100
= 2,601
b. 492 = (50 – 1)2 = 502 + 12 – 2(50)(1)
= 2,500 + 1 – 100
= 2,401
b. (50½) 2 = (50 + ½ )2 = 502 + ½ 2 + 2 (½) (50)
= 2,500 + 1/4 + 50
= 2,550¼

77. Multiplication Formulas
Exercise. A. Calculate. Use the conjugate formula.
1. 21*19 2. 31*29 3. 41*39 4. 71*69
5. 22*18 6. 32*28 7. 52*48 8. 73*67
B. Calculate. Use the squaring formula.
9. 212 10. 312 11. 392 12. 692
13. 982 14. 30½2 15. 100½2 16. 49½2
C. Expand.
18. (x + 5)(x – 5) 19. (x – 7)(x + 7)
20. (2x + 3)(2x – 3) 21. (3x – 5)(3x + 5)
22. (7x + 2)(7x – 2) 23. (–7 + 3x )(–7 – 3x)
24. (–4x + 3)(–4x – 3) 25. (2x – 3y)(2x + 3y)
26. (4x – 5y)(5x + 5y) 27. (1 – 7y)(1 + 7y)
28. (5 – 3x)(5 + 3x) 29. (10 + 9x)(10 – 9x)
30. (x + 5)2 31. (x – 7)2
32. (2x + 3)2 33. (3x + 5y)2
34. (7x – 2y)2 35. (2x – h)2