Section 3.1 Simplifying Expressions and Combining Like Terms 135 Example 4 31x 42 31x2 3142 b. First write the subtraction as addition of the opposite. Apply the distributive property. Simplify. 213y 5z 12 233y 15z2 14 233y 15z2 14 213y2 215z2 2112 6y 110z2 2 6y 10z 2 TIP: In Example 4(b), we rewrote the expression by writing the subtraction as addition of the opposite. Often this step is not shown and fewer steps are shown overall. For example: 213y 5z 12 213y2 215z2 2112 6y 10z 2 Applying the Distributive Property Example 5 Apply the distributive property. a. 812 5y2 b. 14a b 3c2 Solution: a. 812 5y2 832 15y24 Write the subtraction as addition of the opposite. 832 15y24 Apply the distributive property. 8122 18215y2 16 40y Simplify. b. 14a b 3c2 The negative sign preceding the parentheses indicates that we take the opposite of the expression within parentheses. This is equivalent to multiplying the expression within 1 14a b 3c2 parentheses by 1. 114a2 1121b2 11213c2 Apply the distributive property. 4a b 3c Simplify. Skill Practice Apply the distributive property. 11. 412 m2 12. 615p 3q 12 1 14a b 3c2 Answers 11. 8 4m 12. 30p 18q 6 13. 24 40x 14. 2x 3y 4z Applying the Distributive Property Apply the distributive property. a. 31x 42 b. 213y 5z 12 Solution: a. Apply the distributive property. 3x 12 Simplify. Avoiding Mistakes Note that 6y 10z 2 cannot be simplified further because 6y, 10z, and 2 are not like terms. Skill Practice Apply the distributive property. 13. 416 10x 2 14. 12x 3y 4z 2 TIP: Notice that a negative factor outside the parentheses changes the signs of all terms to which it is multiplied. 4a b 3c
miller_prealgebra_2e_ch1_3
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