\(\left(x+y\right)^3-\left(x-y\right)^3\)
\(=\left(x+y-x+y\right)\left[\left(x+y\right)^2+\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\right]\)
\(=2y\left(x^2+2xy+y^2+x^2-y^2+x^2-2xy+y^2\right)\)
\(=2y\left(3x^2+y^2\right)\)
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(x+y)3-(x-y)3
=(x+y-x+y)[(x+y)2+(x+y)(x-y)+(x-y)2]
=2y(x2+2xy+y2+x2-y2+x2-2xy-y2)
=2y(3x2-y2)
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