Section 1.7 Properties of Real Numbers and Simplifying Expressions 83 When we apply the distributive property, the parentheses are removed. Sometimes this is referred to as clearing parentheses. In Examples 10 and 11, we clear parentheses and combine like terms. Clearing Parentheses and Combining Like Terms Simplify by clearing parentheses and combining like terms. Solution: The order of operations indicates that we must perform multiplication before subtraction. It is important to understand that a factor of (not 2) will be multiplied to all terms within the parentheses. To see why this is so, we may rewrite the subtraction in terms of addition. Change subtraction to addition. 5 12213x 72 5 12213x 72 2 A factor of is to be distributed to terms in the parentheses. Apply the distributive property. Simplify. Arrange like terms together. Combine like terms. Simplify by changing addition of the opposite to subtraction. 5 12213x2 122172 5 16x2 1142 5 1142 16x2 9 16x2 9 6x Skill Practice Clear the parentheses and combine like terms. 20. Clearing Parentheses and Combining Like Terms 9 512x 72 Simplify by clearing parentheses and combining like terms. a. b. Solution: a. Simplify fractions. Arrange like terms together. Combine like terms. k 3k 2k 0 2k 1 2 1 2 k 1 2 3k 1 2 4 4 k 2 4 6 2 k 1 2 1 4 14k 22 1 2 16k 12 14s 6t2 13t 5s2 2s 1 4 14k 22 1 2 16k 12 Example 11 2 5 213x 72 5 213x 72 Example 10 Apply the distributive property. Notice that a factor of 12 is distributed through the second parentheses and changes the signs. Answer 20. 10x 44
miller_beginning_intermediate_algebra_4e_ch1_3
To see the actual publication please follow the link above