Holt Algebra 1

1-7 Simplifying Expressions

Use the Commutative, Associative, and Distributive Properties to simplify expressions.

Combine like terms.

Objectives

Holt Algebra 1

1-7 Simplifying Expressions

termlike termscoefficient

Vocabulary

Holt Algebra 1

1-7 Simplifying Expressions

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

Holt Algebra 1

1-7 Simplifying Expressions

Holt Algebra 1

1-7 Simplifying Expressions

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.

4x – 3x + 2

Like terms Constant

Holt Algebra 1

1-7 Simplifying Expressions

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.

1x2 + 3x

Coefficients

Holt Algebra 1

1-7 Simplifying Expressions

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

= (3)x2

= 3x2

Factor out x2 from both terms.

Perform operations in parenthesis.

Notice that you can combine like terms by adding or subtracting the coefficients and keeping the variables and exponents the same.

Holt Algebra 1

1-7 Simplifying Expressions

Example 3A: Combining Like Terms

Simplify the expression by combining like terms.

72p – 25p

72p – 25p

47p

72p and 25p are like terms.

Subtract the coefficients.

Holt Algebra 1

1-7 Simplifying Expressions

Example 3B: Combining Like Terms

Simplify the expression by combining like terms.

A variable without a coefficient has a coefficient of 1.

Write 1 as .

Add the coefficients.

and are like terms.

Holt Algebra 1

1-7 Simplifying Expressions

Example 3C: Combining Like Terms

Simplify the expression by combining like terms.

0.5m + 2.5n

0.5m + 2.5n

0.5m + 2.5n

0.5m and 2.5n are not like terms.

Do not combine the terms.

Holt Algebra 1

1-7 Simplifying Expressions

Check It Out! Example 3

Simplify by combining like terms.

3a. 16p + 84p

16p + 84p

100p

16p + 84p are like terms.

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.

3m2 + m3 3m2 and m3 are not like terms.

3c. 3m2 + m3

Do not combine the terms.3m2 + m3

Holt Algebra 1

1-7 Simplifying Expressions

Example 4: Simplifying Algebraic Expressions

Simplify 14x + 4(2 + x). Justify each step.

14x + 4(2) + 4(x) Distributive Property

Multiply.

Commutative Property

Associative Property

Combine like terms.

14x + 8 + 4x

(14x + 4x) + 8

14x + 4x + 8

18x + 8

14x + 4(2 + x)1. 2. 3. 4. 5. 6.

Procedure Justification

Holt Algebra 1

1-7 Simplifying Expressions

6(x) – 6(4) + 9 Distributive Property

Multiply.Combine like terms.

6x – 24 + 9

6x – 15

6(x – 4) + 91. 2. 3. 4.

Procedure Justification

Check It Out! Example 4a

Simplify 6(x – 4) + 9. Justify each step.

Holt Algebra 1

1-7 Simplifying Expressions

–12x – 5x + x + 3a Commutative Property

Combine like terms.–16x + 3a

–12x – 5x + 3a + x1. 2. 3.

Procedure Justification

Check It Out! Example 4b

Simplify −12x – 5x + 3a + x. Justify each step.

Holt Algebra 1

1-7 Simplifying Expressions

Lesson Quiz: Part II

Simplify each expression by combining like terms. Justify each step with an operation or property.

7. 301x – x

8. 24a + b2 + 3a + 2b2

5.

300x

27a + 3b2

6. 14c2 – 9c 14c2 – 9c