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

Mar 26, 2018

The factored form is $\left(x - 3 y\right) \left(x + y\right)$.

#### Explanation:

You can treat it like a quadratic, where instead of constant numbers, there are $y$ terms.

First, find two numbers that multiply to $- 3$ (the $c$ value of the "quadratic") and add up to $- 2$ (the $b$ value of the "quadratic").

These two numbers are $- 3$ and $1$. Split the middle term into these two numbers. Then, factor the first two and last two terms separately, then combine them:

$\textcolor{w h i t e}{=} {x}^{2} - 2 x y - 3 {y}^{2}$

$= {x}^{2} + x y - 3 x y - 3 {y}^{2}$

$= \textcolor{red}{x} \left(x + y\right) - 3 x y - 3 {y}^{2}$

$= \textcolor{red}{x} \left(x + y\right) \textcolor{b l u e}{-} \textcolor{b l u e}{3 y} \left(x + y\right)$

$= \left(\textcolor{red}{x} \textcolor{b l u e}{-} \textcolor{b l u e}{3 y}\right) \left(x + y\right)$

This is the factored form. Hope this helped!