Question 76737
{{{15 + 3y - 5x^2 - x^2y }}} Start with the given problem
{{{(15 + 3y) + (- 5x^2 - x^2y) }}} group like terms
{{{3(5 + y) -x^2(5 + y) }}} Factor out a 3 out of the first group. Factor out a {{{-x^2}}} our of the second group.
Notice we have a common term of (5+y). If we let w=5+y we get
{{{3w-x^2w}}} Since we have a common term of w, we can combine these terms
{{{(3-x^2)w}}} Combine like terms
{{{(3-x^2)(5+y)}}}replace w with 5+y
So {{{15 + 3y - 5x^2 - x^2y }}} factors to {{{(3-x^2)(5+y)}}}
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Check:
If we foil {{{(3-x^2)(5+y)}}} we should get {{{15 + 3y - 5x^2 - x^2y }}} again.

{{{(3-x^2)(5+y)}}} foil
{{{(3-x^2)(5+y)=3*5+3y-5x^2-x^2y=15+3y-5x^2-x^2y}}} so this supports our answer