1. Simplifying Expressions
1-7
Simplifying Expressions
Holt Algebra 1
Warm Up
Lesson Presentation
Lesson Quiz

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

3. Objectives
Use the Commutative, Associative, and Distributive Properties to simplify expressions.
Combine like terms.

4. Vocabulary
term
like terms
coefficient

6. Example 1A: Using the Commutative and Associative Properties
Simplify.
Use the Commutative Property.
Use the Associative Property to make groups of compatible numbers.
11(5) 55

7. Check It Out! Example 1a
Simplify.
Use the Commutative Property.
Use the Associative Property to make groups of compatible numbers. 21

8. 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.

9. Example 2A: Using the Distributive Property with Mental Math
Write the product using the Distributive Property. Then simplify.
5(59)
5(50 + 9)
Rewrite 59 as
5(50) + 5(9)
Use the Distributive Property.
Multiply.
295
Add.

10. Check It Out! Example 2b
Write the product using the Distributive Property. Then simplify.
12(98)
12(100 – 2)
Rewrite 98 as 100 – 2.
12(100) – 12(2)
Use the Distributive Property.
1200 – 24
Multiply.
1176
Subtract.

11. 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

12. 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

13. 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.

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

15. 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.

16. 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.

17. 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. 3m2 + m3
3m2 and m3 are not like terms.
3m2 + m3
Do not combine the terms.

18. 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.

19. 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.

20. Lesson Quiz: Part I
Simplify each expression.
200 2. 8
Write each product using the Distributive Property. Then simplify.
3. 5($1.99)
5($2) – 5($0.01) = $9.95
4. 6(13)
6(10) + 6(3) = 78

21. 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