Elementary Algebra

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

Chapter 6 - Factoring, Solving Equations, and Problem Solving - Chapter 6 Review Problem Set: 21

Answer

$(4x+5)^{2} $

Work Step by Step

In accordance with the rules of factoring trinomials, we need to find two integers whose product is $16(25)=400$ and whose sum is $40$. A little searching determines that these numbers are $20$ and $20$. Therefore, we can express the middle term, $40x$, as $(20x+20x)$ and proceed to factoring by grouping: $16x^{2}+40x+25$ =$16x^{2}+20x+20x+25$ =$4x(4x+5)+5(4x+5)$ =$(4x+5)(4x+5)$ =$(4x+5)^{2}$
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