How do you factor the trinomial $x^2+15xy+44y^2$ ?

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Answer 1 · 2015-11-26T17:54:25

$(x+4y)(x+11y)$

Straight off you need something like:

$color(blue)((x+-?y)(x+-?y))$ This will give you the $x^2 " and " y^2$ parts

There is no coefficient in front of $x^2$ so they can only be in front of the $y's$

We need an $a " and "b$ such that $ab=44 " and " a+b=15$

They are both the same sign as $ab$ is positive.
They are both positive as $15xy$ is positive.

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Factors of 44 $-> {1,44}, {2,22}, {4,11} ->color(blue)( 4+11=15)color(white)(....)color(red)("looks good!")$

$(x+4y)(x+11y) = x^2 +11xy+4xy+44y^2$

$=x^2+15xy+44y^2 color(white)(....)color(red)("This works")$

How do you factor the trinomial x^2+15xy+44y^2x^2+15xy+44y^2?