# How do you factor 2x^2-98?

##### 1 Answer
Mar 20, 2018

$2 \left(x - 7\right) \left(x + 7\right)$

#### Explanation:

There's a common factor of 2 for both terms, so let's pull that out:
$2 \left({x}^{2} - 49\right)$

Now, we know that $49 = {7}^{2}$, which means that we can use difference of squares! The difference of squares formula is
${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

With $a = x$ and $b = 7$, this tells us that
${x}^{2} - 49 = {x}^{2} - {7}^{2} = \left(x - 7\right) \left(x + 7\right)$

so our final factorization is
$2 {x}^{2} - 98 = 2 \left(x - 7\right) \left(x + 7\right)$