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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 7: Q. 419 (page 899)

Factor Differences of Squares
In the following exercises, factor.
$169 m^{2} - n^{2}$

Short Answer

Expert verified

The factors for $169 m^{2} - n^{2} = (13 m - n) (13 m + n)$

Step by step solution

01

Step 1. Given information

The given differences of squares $169 m^{2} - n^{2}$

02

Step 2. Finding the factors for given differences of squares

We can find the factors as follows

Use the sum product pattern

$169 m^{2} - n^{2} = 169 m^{2} - 13 m n + 13 m n - n^{2}$

Common factors from the two pairs

$169 m^{2} - 13 m n + 13 m n - n^{2} = 13 m (13 m - n) + n (13 m - n)$

Rewrite in factored form

$13 m (13 m - n) + n (13 m - n) = (13 m - n) (13 m + n)$

Therefore,the factors for $169 m^{2} - n^{2} = (13 m - n) (13 m + n)$

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