# How do you factor 42x^2 + 5xy - 25y^2?

Apr 8, 2018

$\left(6 x - 5\right) \left(7 x + 5\right)$

#### Explanation:

$\left(6 x - 5\right) \left(7 x + 5\right)$

You can use the quadratic formula or the cross-multiply rule (i think that's what it's called)

Quadratic formula = $\frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$a = 42 , b = 5 , c = - 25$

$x = \frac{- 5 \pm \sqrt{{5}^{2} - 4 \cdot 42 \cdot - 25}}{2 \cdot 42}$

$x = \frac{- 5 \pm \sqrt{4225}}{84}$

$x = \frac{- 5 \pm 65}{84}$

$x = - \frac{70}{84} = - \frac{5}{6}$ or $x = \frac{60}{84} = \frac{5}{7}$

$\left(x - \frac{5}{6}\right) \left(x + \frac{5}{7}\right)$
=$\left(6 x - 5\right) \left(7 x + 5\right)$