1. Objectives
Combining like terms.

2. The terms of an expression are the parts to be added or subtracted
The terms of an expression are the parts to be added or subtracted. Like terms are terms that contain the same variables raised to the same powers. Constants are also like terms.
Like terms
Constant
4x – 3x + 2

3. A coefficient is a number multiplied by a variable
A coefficient is a number multiplied by a variable. Like terms can have different coefficients. A variable written without a coefficient has a coefficient of 1.
Coefficients
1x2 + 3x

4. Example 3A: Combining Like Terms
Simplify the expression by combining like terms.
7p – 5p
18y2 + 2y2
13w3 – 4w
7p – 5p
18y2 + 2y2
13w3 – 4w 2p
20y2
13w3 – 4w

5. Example 3A: Combining Like Terms
Simplify the expression by combining like terms.
12m + 4n
8r3 + 3r3
10a – 7a
12m + 4n
8r3 + 3r3
10a – 7a
12m + 4n
11r3 3a

6. Example 3C: Combining Like Terms
Simplify the expression by combining like terms.
5m + 2 – 3m
20t2 + 6t + 4t – 15t2
5m + 2 – 3m
20t2 + 6t + 4t – 15t2
2m + 2
5t2 + 6t + 4t
5t2 + 10t

7. Example 4: Simplifying Algebraic Expressions
Simplify 7x + 4(3 + 2x). Justify each step.
Procedure
Justification 1.
7x + 4(3 + 2x) 2.
7x + 4(3) + 4(2x)
Distributive Property 3.
7x x
Multiply.
Commutative Property 4.
7x + 8x + 12 5.
(7x + 8x) + 12
Associative Property 6.
15x + 12
Combine like terms.

8. Check It Out! Example 4a
Simplify -6(x – 4) + 9. Justify each step.
Procedure
Justification 1.
-6(x – 4) + 9 2.
-6(x) – 6(-4) + 9
Distributive Property 3.
-6x
Multiply.
Combine like terms. 4.
-6x + 33

9. Check It Out! Example 4b
Simplify −12x – 5x + 3a + x. Justify each step.
Procedure
Justification 1.
–12x – 5x + 3a + x 2.
–17x + x + 3a
Commutative Property 3.
–16x + 3a
Combine like terms.

10. Lesson Quiz: Part II
Simplify each expression by combining like terms. Justify each step with an operation or property. 5.
6. 14c2 – 9c
14c2 – 9c
7. -2(3x – 4) + 2x
(-6x + 8) + 2x = -4x + 8
8. 24a + b2 + 3a + 2b2
27a + 3b2