Question

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

Answer 1

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)`