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: 34



Work Step by Step

$\bf{\text{Solution Outline:}}$ To factor the given expression, $ (x+y)^2+6(x+y)+9 ,$ 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 $z= (x+y) .$ The given expression becomes \begin{array}{l}\require{cancel} z^2+6z+9 .\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+3)^2 .\end{array} Since $z= (x+y) ,$, then the expression above becomes \begin{array}{l}\require{cancel} ((x+y)+3)^2 \\\\ (x+y+3)^2 .\end{array}
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.