College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Chapter P Review - Exercises - Page 77: 70



Work Step by Step

RECALL: (1) $(a+b)(c+d) = ac +ad + bc + bd$ (known as the FOIL method) (2) $(a-b)(a+b)=a^2-b^2$ Use the formula (1) above to multiply the first pair of factors, and use formula (2) to multiply the second pair of factors to obtain: $=[1\cdot2 + 1\cdot(-x) + x \cdot 2 + x\cdot(-x)] -(3^2 - x^2) \\=(2 -x+2x-x^2)-(9-x^2) \\=(2+x-x^2)-(9-x^2)$ Subtract each term of the subtrahend to obtain: $=2+x-x^2-9-(-x^2) \\=2+x-x^2-9+x^2$ Combine like terms to obtain: $=(2-9)+x+(-x^2+x^2) \\=-7+x \\=x-7$
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