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

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Answer 1 · 2015-03-24T02:39:04

Remember that for the general case
$(x+ay) * (x+by) = (x^2 + (a+b)xy + (ab)y^2)$
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
$ab = 2$

The obvious pair is $(1,2)$
so
$x^2+3xy+2y^2 = (x+y)(x+2y)$

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