How do you simplify and divide #(x^3+y^3)div(x+y)#?

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Answer 1 · 2016-12-12T06:11:38

The answer is #=x^2-xy+y^2#

We know that

#a^3+b^3=(a+b)(a^2-ab+b^2)#

So,

#(x^3+y^3)=(x+y)(x^2-xy+y^2)#

Therefore,

#(x^3+y^3)/(x+y)=(cancel(x+y)(x^2-xy+y^2))/cancel(x+y)#

#=x^2-xy+y^2#