Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter R - Review of Basic Concepts - R.4 Factoring Polynomials - R.4 Exercises: 69

Answer

$\color{}(x+y-4)(x-y-4)$

Work Step by Step

Group the first three terms together to obtain: $=(x^2-8x+16)-y^2$ The trinomial is a perfect square trinomial in the form $a^2-2ab+b^2$ with $a=x$ and $b=4$. RECALL: $a^2-2ab+b^2=(a-b)^2$ Use the formula above to obtain: $=(x-4)^2-y^2$ The polynomial above is a difference of two squares. Factor using the formula $a^2-b^2=(a-b)(a+b)$ with $a=x-4$ and $b=y$ to obtain: $=[(x-4)+y][(x-4)-y] \\=(x-4+y)(x-4-y) \\=\color{}(x+y-4)(x-y-4)$
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