Question

Factor Differences of Squares

In the following exercises, factor.

$169m^2-n^2$

Short answer

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

Step-by-step solution

Step 1. Given information

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

Step 2. Finding the factors for given differences of squares

We can find the factors as follows

Use the sum product pattern

$169m^2-n^2=169m^2-13mn+13mn-n^2$

Common factors from the two pairs

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

Rewrite in factored form

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

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