## Elementary Algebra

Published by Cengage Learning

# Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.5 - Factoring, Solving Equations, and Problem Solving - Problem Set 6.5 - Page 269: 3

#### Answer

$x^2-10x+25=(x-5)^2$

#### 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: $x^2-2(x)(5)+5^2$ Factor this perfect square trinomial using formula (ii) above where $a=x$ and $b=5$ to obtain: $x^2-2(x)(5)+5^2=(x-5)^2$ Therefore, $x^2-10x+25=(x-5)^2$

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.