Question

Factor Differences of Squares

In the following exercises, factor.

$49a^2-144$

Short answer

The factors of$49a^2-144=(7a+12)(7a-12)$

Step-by-step solution

Step 1. Given information

The given differences of squares$49a^2-144$

Step 2. Finding the factors for given differences of squares

We can find the factors as follows

Use the sum product pattern

$49a^2-144=49a^2+84a-84a-144$

Common factors from the two pairs

$7a(7a+12)-12(7a+12)$

Rewrite in factored form

$(7a+12)(7a-12)$

Therefore,the factors of$49a^2-144=(7a+12)(7a-12)$