1. Warm Up
Add.
462
1.80 3. 10
Multiply.
4. 25(8)
200
5. 1.3(22)
28.6 6.

2. The Distributive Property is used with Addition to Simplify Expressions.
The Distributive Property also works with subtraction because subtraction is the same as adding the opposite.

3. 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

4. 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

5. Using the Distributive Property can help you combine like terms
Using the Distributive Property can help you combine like terms. You can factor out the common factors to simplify the expression.
7x2 – 4x2 = (7 – 4)x2
Factor out x2 from both terms.
= (3)x2
Perform operations in parenthesis.
= 3x2
Notice that you can combine like terms by adding or subtracting the coefficients and keeping the variables and exponents the same.

6. Example 3A: Combining Like Terms
Simplify the expression by combining like terms.
72p – 25p
72p – 25p
72p and 25p are like terms.
47p
Subtract the coefficients.

7. Example 3B: Combining Like Terms
Simplify the expression by combining like terms.
A variable without a coefficient has a coefficient of 1.
and are like terms.
Write 1 as .
Add the coefficients.

8. Example 3C: Combining Like Terms
Simplify the expression by combining like terms.
0.5m + 2.5n
0.5m + 2.5n
0.5m and 2.5n are not like terms.
0.5m + 2.5n
Do not combine the terms.

9. Check It Out! Example 3
Simplify by combining like terms.
3a. 16p + 84p
16p + 84p
16p + 84p are like terms.
100p
Add the coefficients.
3b. –20t – 8.5t2
–20t – 8.5t2
20t and 8.5t2 are not like terms.
–20t – 8.5t2
Do not combine the terms.
3c. 3m2 + m3
3m2 + m3
3m2 and m3 are not like terms.
3m2 + m3
Do not combine the terms.

10. Example 4: Simplifying Algebraic Expressions
Simplify 14x + 4(2 + x). Justify each step.
Procedure
Justification 1.
14x + 4(2 + x) 2.
14x + 4(2) + 4(x)
Distributive Property 3.
14x x
Multiply.
Commutative Property 4.
14x + 4x + 8 5.
(14x + 4x) + 8
Associative Property 6.
18x + 8
Combine like terms.

11. 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 – 15

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

13. 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. 301x – x
300x
8. 24a + b2 + 3a + 2b2
27a + 3b2