Question

Factor Differences of Squares

In the following exercises, factor.

$25p^2-1$

Short answer

The factors for$25p^2-1=(5p+1)(5p-1)$

Step-by-step solution

Step 1. Given information

The given differences of squares$25p^2-1$

Step 2. Finding the factors for given differences of squares

We can find the factors as follows

Use the sum product pattern

$25p^2-1=25p^2+5p-5p+1$

Common factors from the two pairs

$5p(5p+1)-1(5p+1)$

Rewrite in factored form

$(5p+1)(5p-1)$

Therefore,the factors of$25p^2-1=(5p+1)(5p-1)$