136 Chapter 3 Solving Equations 3. Combining Like Terms Two terms may be combined if they are like terms. To add or subtract like terms, we use the distributive property as shown in Example 6. Using the Distributive Property to Add and Subtract Like Terms Example 6 Add or subtract as indicated. a. 8y 6y b. 7x2y 10x2y c. 15w 4w w Solution: a. Apply the distributive property. Simplify. 8y 6y 18 62y 7x2y 10x2y 17 102x2y b. Apply the distributive property. Simplify. 3x2y c. First note that w 1w. Apply the distributive property. Simplify within parentheses. 15w4w w15w 4w 1w 115 4 12w 1122w Although the distributive property is used to add and subtract like terms, it is tedious to write each step. Observe that adding or subtracting like terms is a matter of adding or subtracting the coefficients and leaving the variable factors unchanged. This can be shown in one step. 8y 6y 14y and 15w 4w 1w 12w This shortcut will be used throughout the text. Adding and Subtracting Like Terms Simplify by combining like terms. Solution: Rewrite subtraction as addition of the opposite. Use the commutative and associative properties of addition to arrange terms so that like terms are grouped together. Combine like terms. Note that 1x x. Also note that the remaining terms cannot be combined further because they are not like. The variable factors are different. 3x 8y 4x 19 10y 3x 8y 4x 1192 110y2 3x 4x 8y 110y2 1192 1x 2y 19 x 2y 19 3x 8y 4x 19 10y Example 7 12w 14y Skill Practice Add or subtract as indicated. 15. 4w 11w 16. 6a3b2 11a3b2 17. z 4z 22z Skill Practice Simplify. 18. 4a 10b a 16b 9 Answers 15. 7w 16. 5a3b2 17. 19z 18. 3a 6b 9
miller_prealgebra_2e_ch1_3
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