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: 57



Work Step by Step

Test whether this is a perfect square, $(A-B)^{2}=A^{2}-2AB+B^{2}$ First term: $A^{2}=(a-3b)^{2}\Rightarrow A=a-3b$ Third term: $B^{2}=(3)^{2}\Rightarrow B=3$ Test:$\qquad$ does $-2AB$ equal the middle term? $-2AB=-2(a-3b)(3)=-6(a-3b)\qquad$ ... yes, it does. $\Rightarrow$This is a perfect square, $[(a-3b)-3]^{2}=(a-3b-3)^{2}$
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