Question 156798: Please help me solve:
(x-y)^3-(x+y)^3
I belive this is the difference of perfect cubes, however, I'm not sure how to write it out!! Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! Yes, you are correct.
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See:
http://www.purplemath.com/modules/specfact2.htm
for detailed information
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The special case is:
a^3 – b^3 = (a – b)(a^2 + ab + b^2)
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In your case:
(x-y)^3-(x+y)^3
'a' is (x-y)
'b' is (x+y)
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Therefore,
(x-y)^3-(x+y)^3
= ((x-y)-(x+y))((x-y)^2 + (x-y)(x+y) + (x+y)^2)
= (x-y-x-y)((x-y)^2 + (x-y)(x+y) + (x+y)^2)
= (-2y)((x-y)^2 + (x-y)(x+y) + (x+y)^2)
= (-2y)((x^2-2xy+y^2) + (x^2-y^2) + (x^2+2xy+y^2))
= (-2y)(x^2-2xy+y^2 + x^2-y^2 + x^2+2xy+y^2)
= (-2y)(x^2 + x^2 + x^2+y^2)
= (-2y)(3x^2 + y^2)
