# Question #73265

Jun 1, 2017

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

#### Explanation:

Treat this like a quadratic of the form $a {x}^{2} + b x + c$.

$a = 2$
$b = y$
$c = - {y}^{2}$

Now, to factor, we need to find 2 factors of $a c$ which add up to $b$.

$a c = 2 \left(- {y}^{2}\right) = - 2 {y}^{2}$

We can use $2 y$ and $- y$, since $2 y \left(- y\right) = - 2 {y}^{2}$ and $2 y + \left(- y\right) = y$. This satisfies both conditions of multiplying to make $a c$ and adding up to $b$.

Our factored form will look like this:

$a \left(x + \frac{\text{factor 1"/a)(x+"factor 2}}{a}\right)$

$2 \left(x + \frac{2 y}{2}\right) \left(x + \frac{- y}{2}\right)$

$2 \left(x + y\right) \left(x - \frac{y}{2}\right)$

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