Question

Factor Differences of Squares

In the following exercises, factor.

$18y^2-98$

Short answer

The factors for$18y^2-98=2(3y+7)(3y-7)$

Step-by-step solution

Step 1. Given information

The given differences of squares$18y^2-98$

Step 2. Finding the factors for given differences of squares

Take 2 as common from given differences of squares as $18y^2-98=2(9y^2-49)$

We can find the factors as follows

Use the sum product pattern

$2(9y^2-49)=2(9y^2+21y-21y-49)$

Common factors from the two pairs

$2\left(3y\right(3y+7)-7(3y+7\left)\right)$

Rewrite in factored form

$2(3y+7)(3y-7)$

Therefore,the factors for$18y^2-98=2(3y+7)(3y-7)$