Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.5 - Factoring, Solving Equations, and Problem Solving - Problem Set 6.5: 2

Answer

$(x+9)^2$

Work Step by Step

RECALL: Perfect square trinomials can be factored using the following formulas: (i) $a^2+2ab+b^2 = (a+b)^2$ (ii) $a^2-2ab+b^2=(a-b)^2$ The given perfect square trinomial can be written as: $x^2 + 2(x)(9) + 9^2$ Factor this perfect square trinomial using formula (i) above where $a=x$ and $b=9$ to obtain: $x^2 + 2(x)(9) + 9^2 = (x+9)^2$ Therefore, $x^2+18x+81 = (x+9)^2$
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