Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter P - Section P.5 - Factoring Polynomials - Exercise Set - Page 69: 110

Answer

$(x-3y)(x+3y)(x-y)(x+y)$

Work Step by Step

Treat as a trinomial of the form $t^{2}+bt+c,$ where $t=x^{2}$ $=t^{2}-10y^{2}\cdot t+9y^{4}$ we search for factors of $c=9y^{2}$ whose sum is $b=-10y^{2}$ and we find $-9y^{2}$ and $-y^{2}$ $= (t-9y^{2})(t-y^{2})\quad$ ... bring back x, $=(x^{2}-9y^{2})(x^{2}-y^{2})\quad$ recognize two differences of squares = $(x-3y)(x+3y)(x-y)(x+y)$
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