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Q. 103

Expert-verified

Elementary Algebra

Found in: Page 832

Book edition 2nd

Author(s) Lynn Marecek, MaryAnne Anthony-Smith

Pages 1240 pages

ISBN 9780998625713

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Short Answer

In the following exercises, factor each trinomial of the form $x^{2} + b x y + c y^{2}$
$x^{2} - 2 x y - 80 y^{2}$

The factorization of $x^{2} - 2 x y + 80 y^{2}$ is $(x + 8 y) (x - 10 y)$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information

Given expression is $x^{2} - 2 x y - 80 y^{2}$

Step 2. Find the last terms of the trinomials.

The factors of the expression:

The factors of -80	Sum of factors
2, -40	2 + (-40) = -38
4, -20	4 + (-20) = -16
8, -10	8 + (-10) = -2
16, -5	16 + (-5) = 11

Step 3. Factorization

Use $8$ and $- 10$ as the last terms of the trinomials.

$x^{2} - 2 x y - 80 y^{2} = (x + 8 y) (x - 10 y)$

Step 4. Check

$(x + 8 y) (x - 10 y) = x^{2} + 8 x y - 10 x y - 80 y^{2} = x^{2} - 2 x y - 80 y^{2}$

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