divide-x-6-y-6-by-the-product-of-x-2-x-y-y-2-and-x-y-

Question Number 26694 by shiv15031973@gmail.com last updated on 28/Dec/17

d i v i d e x^{6} - y^{6} b y t h e p r o d u c t o f x^{2} + x^{} y + y^{2} a n d x - y .

Answered by Rasheed.Sindhi last updated on 28/Dec/17

Product of (x^{2} + xy + y^{2}) & (x - y)

(x^{2} + xy + y^{2}) (x - y) = x^{3} - y^{3}

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(x^{6} - y^{6}) \div (x^{3} - y^{3})

\frac{{(x^{3})}^{2} - {(y^{3})}^{2}}{x^{3} - y^{3}} = \frac{\overset{\times}{(x^{3} - y^{3})} (x^{3} + y^{3})}{\overset{\times}{(x^{3} - y^{3})}}

= x^{3} + y^{3}