Holt Algebra Simplifying Expressions Use the Commutative, Associative, and Distributive Properties to simplify expressions. Combine like terms. Objectives

Holt Algebra Simplifying Expressions term like terms coefficient Vocabulary

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

Holt Algebra Simplifying Expressions

Holt Algebra 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 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. 1x 2 + 3x Coefficients

Holt Algebra Simplifying Expressions Using the Distributive Property can help you combine like terms. You can factor out the common factors to simplify the expression. 7x 2 – 4x 2 = (7 – 4)x 2 = (3)x 2 = 3x 2 Factor out x 2 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 Simplifying Expressions Example 3A: Combining Like Terms Simplify the expression by combining like terms. 72p – 25p 47p 72p and 25p are like terms. Subtract the coefficients.

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

Holt Algebra 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 – 8.5t 2 –20t – 8.5t 2 20t and 8.5t 2 are not like terms. –20t – 8.5t 2 Do not combine the terms. 3m 2 + m 3 3m 2 and m 3 are not like terms. 3c. 3m 2 + m 3 Do not combine the terms. 3m 2 + m 3

Holt Algebra 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 x (14x + 4x) x + 4x x x + 4(2 + x) Procedure Justification

Holt Algebra Simplifying Expressions 6(x) – 6(4) + 9 Distributive Property Multiply. Combine like terms. 6x – x – 15 6(x – 4) Procedure Justification Check It Out! Example 4a Simplify 6(x – 4) + 9. Justify each step.

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

Holt Algebra Simplifying Expressions Lesson Quiz: Part II Simplify each expression by combining like terms. Justify each step with an operation or property x – x 8. 24a + b 2 + 3a + 2b x 27a + 3b c 2 – 9c 14c 2 – 9c