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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}$${p}^{2}-8pq-65{q}^{2}$

The factorization of ${p}^{2}-8pq-65{q}^{2}$ is $\left(p+5q\right)\left(p-13q\right)$

See the step by step solution

## Step 1. Given information

Given expression is ${p}^{2}-8pq-65{q}^{2}$

## Step 2. Find the last terms of the trinomials.

The factors of the expression:

 The factor of -65 Sum of factor 5, -13 5 + (-13) = -8
 13, -5 13 +(-5) = 8

## Step 3. factorization

Use $5$and $-13$as the last terms of the trinomials.

${p}^{2}-8pq-65{q}^{2}=\left(p+5q\right)\left(p-13q\right)$

## Step 4. Check

$\left(p+5q\right)\left(p-13q\right)={p}^{2}+5pq-13pq-65{q}^{2}\phantom{\rule{0ex}{0ex}}={p}^{2}-8pq-65{q}^{2}$ ### Want to see more solutions like these? 