Section 3.1 Simplifying Expressions and Combining Like Terms 137 4. Simplifying Expressions For expressions containing parentheses, it is necessary to apply the distributive property before combining like terms. This is demonstrated in Examples 8 and 9. Notice that when we apply the distributive property, the parentheses are dropped. This is often called clearing parentheses. Clearing Parentheses and Combining Like Terms Example 8 Simplify by clearing parentheses and combining like terms. Solution: 6 312y 92 The order of operations indicates that we must perform multiplication before subtraction. 6 312y 92 It is also important to understand that a factor of 3 (not 3) will be multiplied to all terms within the parentheses. To see why, we can rewrite the subtraction in terms of addition of the opposite. Rewrite subtraction as addition of the opposite. Apply the distributive property. Simplify. Group like terms together. Combine like terms. 6 312y 92 6 132 12y 92 6 132 12y2 132 192 6 16y2 1272 6y 6 1272 6y 1212 or 6y 21 Clearing Parentheses and Combining Like Terms Example 9 Simplify by clearing parentheses and combining like terms. Solution: Rewrite subtraction as addition of the opposite. Apply the distributive property. Simplify. Group like terms together. 81x 42 15x 72 81x 42 15x 72 83x 142 4 112 15x 72 83x 142 4 112 15x 72 81x2 182 142 112 15x2 112 172 8x 32 15x2 172 8x 15x2 32 172 13x 25 Combine like terms. Skill Practice Simplify. 19. 8 61w 42 Avoiding Mistakes Multiplication is performed before subtraction. It is incorrect to subtract 6 3 first. Skill Practice Simplify. 20. 5110 m2 21m 12 Answers 19. 6w 16 20. 3m 52
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