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

5. The Commutative and Associative Properties of Addition and Multiplication allow you to rearrange an expression to simplify it.

7. 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

8. Example 1B: Using the Commutative and Associative Properties
Simplify.
Use the Commutative Property.
( ) + (16 + 4)
Use the Associative Property to make groups of compatible numbers.
(100) + (20)
120

9. Compatible numbers help you do math
Helpful Hint
Compatible numbers help you do math
mentally. Try to make multiples of 5
or 10. They are simpler to use when
multiplying.

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

11. Check It Out! Example 1b
Simplify.
Use the Commutative Property.
Use the Associative Property to make groups of compatible numbers.
( ) + (58 + 2)
(500) + (60)
560

12. ( ) Check It Out! Example 1c Simplify. 1 2 7 • 8 1 2 8 • 7
Use the Commutative Property. ( ) 1 2 • 8 7
Use the Associative Property to make groups of compatible numbers. 4 • 7 28

13. 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.

14. 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.

15. Example 2B: Using the Distributive Property with Mental Math
Write the product using the Distributive Property. Then simplify.
8(33)
8(30 + 3)
Rewrite 33 as
8(30) + 8(3)
Use the Distributive Property.
Multiply.
264
Add.

16. Check It Out! Example 2a
Write the product using the Distributive Property. Then simplify.
9(52)
9(50 + 2)
Rewrite 52 as
9(50) + 9(2)
Use the Distributive Property.
Multiply.
468
Add.

17. 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.

18. Check It Out! Example 2c
Write the product using the Distributive Property. Then simplify.
7(34)
7(30 + 4)
Rewrite 34 as
7(30) + 7(4)
Use the Distributive Property.
Multiply.
238
Add.

19. 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

20. 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

21. 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.

22. 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.

23. 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.

24. 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.

25. 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.

26. 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.

27. 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

28. 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.

29. 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

30. 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