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: 6

Answer

$25n^2+30n+9=(5n+3)^2$

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: $(5n)^2+2(5n)(3)+3^2$ Factor this perfect square trinomial using formula (i) above where $a=5n$ and $b=3$ to obtain: $(5n)^2+2(5n)(3)+3^2=(5n+3)^2$ Therefore, $25n^2+30n+9=(5n+3)^2$
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