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Find the product of $x+y$ and ${x}^{2}-xy+{y}^{2}$
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= (x+y)(x^2 - xy +y^2)

= x^3 - x^2y +  xy^2 +yx^2 - xy^2 + y^3, you can jump this expansion stage if had known that this is factorized form of sum of 2 cubes and go straight to answer:

= x^3 + y^3
by Diamond (44,166 points)

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