Question

Factor Differences of Squares

In the following exercises, factor.

$169n^3-n$

Short answer

The factors for $169n^3-n=n(13n+1)(13n-1)$

Step-by-step solution

Step 1. Given information

The given differences of squares$169n^3-n$

Step 2. Finding the factors for given differences of squares

Take nas common from given differences of squares$169n^3-n=n(169n^2-1)$

We can find the factors as follows

Use the sum product pattern

$n(169n^2-1)=n(169n^2+13n-13n-1)$

Common factors from the two pairs

$n\left(13n\right(13n+1)-1(13n+1\left)\right)$

Rewrite in factored form

$n(13n+1)(13n-1)$

Therefore,the factors for$169n^3-n=n(13n+1)(13n-1)$