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")#