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

Mar 24, 2015

Remember that for the general case
$\left(x + a y\right) \cdot \left(x + b y\right) = \left({x}^{2} + \left(a + b\right) x y + \left(a b\right) {y}^{2}\right)$
which is a result with the same form as the given expression

provided we can find two values for $a$ and $b$ such that
$a + b = 3$ and
$a b = 2$

The obvious pair is $\left(1 , 2\right)$
so
${x}^{2} + 3 x y + 2 {y}^{2} = \left(x + y\right) \left(x + 2 y\right)$