Question 236035: can you help me factor
4x^3+4x^2y-24xy^2
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 4x^3+4x^2y-24xy^2
factor out 4x to get:
4x * (x^2 + xy - 6y^2)
if you didn't have the y there, your equation within the parentheses would have been:
x^2 + x - 6 which factors as (x+3) * x-2)
if you add a y into the right side of each of the factors, you get:
x^2 + xy - 6y^2 = (x+3y) * (x-2y)
this looks like it will actually work.
your factors should be:
4x * (x+3y) * (x-2y)
to confirm they are good, work back to see if you can get the original equation again.
(x + 3y) * (x-2y) becomes:
x^2 - 2xy + 3xy - 6y^2 which becomes
x^2 + xy - 6y^2
multiply that by 4x to get:
4x * (x^2 + xy - 6y^2) becomes:
4x^3 + 4x^2y - 24xy^2
your original equation is:
4x^3 + 4x^2y - 24xy^2
since they're the same, your answer is confirmed.
your answer is:
4x * (x+3y) * (x-2y)
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