Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter R - Review of Basic Concepts - R.4 Factoring Polynomials - R.4 Exercises - Page 44: 53



Work Step by Step

Factor out the greatest common factor, $2$ $32a^{2}+48ab+18b^{2}=2(16a^{2}+24ab+9b^{2})=*$ Test whether the parentheses hold a perfect square, $(A+B)^{2}=A^{2}+2AB+B^{2}$ First term: $A^{2}=(4a)^{2}\Rightarrow A=4a$ Third term: $B^{2}=(3b)^{2}\Rightarrow B=3b$ Test:$\qquad$ does $2AB$ equal the middle term? $ 2AB=2(4a)(3b)=24ab\qquad$ ... yes, it does. The parentheses hold a perfect square, $(4a+3b)^{2}$ $*...= 2(4a+3b)^{2}$
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