# How do you factor -7x^2+175?

May 12, 2018

Prime factorize them
$- 7 {x}^{2} = - 1 \times 7 \times x \times x$
$175 = 5 \times 5 \times 7$
As you can see... both have 7 as common
$7 \left(- {x}^{2} + 25\right)$
Leaving it like this will not complete the answer
Notice
$7 \left(25 - {x}^{2}\right) = 7 \left({5}^{2} - {x}^{2}\right)$

This is a law of exponents
${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$

Here... $5 = a , x = b$
$7 \left({5}^{2} - {x}^{2}\right) = 7 \left(5 + x\right) \left(5 - x\right)$

May 12, 2018

$- 7 \left(x - 5\right) \left(x + 5\right)$

#### Explanation:

$- 7 {x}^{2} + 175$

Factor out the $- 7$

=$- 7 \left({x}^{2} - 25\right)$

Using the rule difference of two squares: $\left(x - a\right) \left(x + a\right) = {x}^{2} - {a}^{2}$

=$- 7 \left(x - 5\right) \left(x + 5\right)$