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Expert-verified Found in: Page 832 ### Elementary Algebra

Book edition 2nd
Author(s) Lynn Marecek, MaryAnne Anthony-Smith
Pages 1240 pages
ISBN 9780998625713 # In the following exercises, factor each trinomial of the form ${x}^{2}+bxy+c{y}^{2}$${x}^{2}-2xy-80{y}^{2}$

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

See the step by step solution

## Step 1. Given information

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

## 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.

${x}^{2}-2xy-80{y}^{2}=\left(x+8y\right)\left(x-10y\right)$

## Step 4. Check

$\left(x+8y\right)\left(x-10y\right)={x}^{2}+8xy-10xy-80{y}^{2}\phantom{\rule{0ex}{0ex}}={x}^{2}-2xy-80{y}^{2}$ ### Want to see more solutions like these? 