Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 5 - Section 5.3 - Special Factoring - 5.3 Exercises - Page 343: 36



Work Step by Step

$\bf{\text{Solution Outline:}}$ To factor the given expression, $ (m-n)^2+4(m-n)+4 ,$ simplify the expression using substitution. The resulting expression is a perfect square trinomial. Use the factoring of perfect square trinomials. Finally, substitute back the original expression. $\bf{\text{Solution Details:}}$ Let $z= (m-n) .$ The given expression becomes \begin{array}{l}\require{cancel} z^2+4z+4 .\end{array} The trinomial above is a perfect square trinomial. Using $a^2\pm2ab+b^2=(a\pm b)^2,$ the expression above is equivalent to \begin{array}{l}\require{cancel} (z+2)^2 .\end{array} Since $z= (m-n) ,$, then the expression above becomes \begin{array}{l}\require{cancel} ((m-n)+2)^2 \\\\ (m-n+2)^2 .\end{array}
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