Math expressions

1. Combine Like TermsCombine Like Terms
I can simplify expressions with severalI can simplify expressions with several
variables by combining like terms.variables by combining like terms.

2. VocabularyVocabulary
ConstantConstant
A number with nothing else attached toA number with nothing else attached to
it.it.
Examples: 1, 2, 47, 925Examples: 1, 2, 47, 925

3. VocabularyVocabulary
VariableVariable
A letter that represents an unknownA letter that represents an unknown
number.number.
Examples: a, b, x, yExamples: a, b, x, y

4. VocabularyVocabulary
CoefficientCoefficient
The number in front of the variable.The number in front of the variable.
Examples: 3x 3 is the coefficientExamples: 3x 3 is the coefficient
2x 2 is the coefficient2x 2 is the coefficient

5. Like Terms:
– In an expression, like terms are the
terms that have the same variables,
raised to the same powers (same
exponents).
• Examples: 4x and -3x or 2y2
and –
y2

6. • Like terms because each term consists
of a single variable, x, and a numeric
coefficient:
2x, 45x, x, 0x, -26x, -x
• Like terms because they are all
constants:
15, -2, 27, 9043, 0.6
• Like terms because they are all y² with
a coefficient: 3y², y², -y², 26y²

7. What are unlike terms?
• The following two terms both have a single
variable, but the terms are not alike since
different variables are used: 17x, 17z
• Each y variable in the terms below has a
different exponent, therefore these are unlike
terms: 15y, 19y², 31y5
• Although both terms below have an x variable,
only one term has the y variable, thus these
are not like terms either: 19x, 14xy

8. Combine Like TermsCombine Like Terms
I can simplify expressions with severalI can simplify expressions with several
variables by combining like terms.variables by combining like terms.

9. Like Terms – same variable
with same exponent
6x + 2x =
When combining like terms,
only use the coefficients.
6x + 2x = 8x
4x + 3y – 2x + 4y =
Simplify
2x + 7y
Simplify
Never, NEVER, combine x’s and y’s or constant terms
with variable terms. 2x + 7y ≠ 9xy and 3a + 6 ≠ 9a.
Key Skills

10. 5 cats + 3 cats5 cats + 3 cats
8 cats8 cats

11. 5a + 3a5a + 3a
8a8a

12. 5 apples + 3 oranges5 apples + 3 oranges
5 apples + 3 oranges5 apples + 3 oranges

13. 5 cats + 3 dogs5 cats + 3 dogs
5 cats + 3 dogs5 cats + 3 dogs

14. You Try
• 3y + 2 + 3x – y + 5x
• x + x

15. Distribute by multiplication:Distribute by multiplication:
15n and 20 are not alike and therefore cannot be combined. The answer 15n + 20 is
simplified because we do not know what the value of n is at this time and cannot
complete the multiplication part of this problem.
15n and 20 are not alike and therefore cannot be combined. The answer 15n + 20 is
simplified because we do not know what the value of n is at this time and cannot
complete the multiplication part of this problem.
=+ )43(5 n )3(5 n
+
)4(5+
= n15 20
The Distributive
Property
• Expressions with variables:
Simplify 5(3n + 4).
• No symbol between the 5 and the parenthesis
indicates a multiplication problem.

16. The constant terms 8 and 6 can be combined to form the constant number 14. The
answer 28n + 14 is simplified because we do not know what the value of n is at
this time and cannot complete the multiplication part of this problem.
The constant terms 8 and 6 can be combined to form the constant number 14. The
answer 28n + 14 is simplified because we do not know what the value of n is at
this time and cannot complete the multiplication part of this problem.
=++ 6)27(4 n )7(4 n
+
)2(4+
= n28 8
+ 6
+ 6
= n28 + 14
The Distributive
Property
• Simplify 4(7n + 2) + 6.
• No symbol between the 4 and the
parenthesis indicates a multiplication
problem.

17. Step 1) Use the Distributive Property 3 (2x – 5) - 2x
Step 2) Combine Like Terms 6x – 15 – 2x
*** 6x and 2x are like terms!!!!
Step 3) Simplified Expression 4x – 15
Distributive Property

18. Distributive Property
Example:
6(a + 3) Use the Distributive Property
(6a) + (6 x 3) Multiply
6a + 18 Simplified
***CAN NOT add 6a + 18 together because they are
not like terms.

19. Solve: 2x + 6(x + 1)
Explain how each of the below answers
are wrong and why.
• 2x + 6x + 1
• 9x
Practice Problems