# How do you factor 3x^2 +10xy -25y^2?

Jul 6, 2015

$3 {x}^{2} + 10 x y - 25 {y}^{2} = \left(3 x - 5 y\right) \left(x + 5 y\right)$

#### Explanation:

If $3 {x}^{2} + 10 x y - 25 {y}^{2}$ has factors with integer coefficients, then they will take the form:

$3 {x}^{2} + 10 x y - 25 {y}^{2} = \left(3 x + a y\right) \left(x + b y\right)$

$= 3 {x}^{2} + \left(3 b + a\right) x y + a b {y}^{2}$

Since $a b = - 25$, the possible $\left(a , b\right)$ values are:

$\left(- 25 , 1\right)$, $\left(- 5 , 5\right)$, $\left(- 1 , 25\right)$, $\left(1 , - 25\right)$, $\left(5 , - 5\right)$, $\left(25 , - 1\right)$

These give values for $3 b + a$ of:

$- 22$, $10$, $74$, $- 74$, $- 10$, $22$

So choose $a = - 5$ and $b = 5$ to get the correct coefficient of $x y$