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 - Page 44: 71



Work Step by Step

Group the last three terms together to obtain: $y^2-x^2+12x-36=y^2-(x^2-12x+36)$ The trinomial is a perfect square trinomial in the form $a^2-2ab+b^2$ with $a=x$ and $b=6$. RECALL: $a^2-2ab+b^2=(a-b)^2$ Use the formula above to obtain: $=y^2-(x-6)^2$ The polynomial above is a difference of two squares. Factor using the formula $a^2-b^2=(a+b)(a-b)$ with $a=y$ and $b=x-6$ to obtain: $=[y+(x-6)][y-(x-6)] \\=\color{blue}{(y+x-6)(y-x+6)}$
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