Verify (i) $x^{3} + y^{3} = (x + y) (x^{2} + x y + y^{2})$

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Solution

R.H.S
$\Rightarrow (x + y) (x^{2} - x y + y^{2})$
$\Rightarrow (x^{3} - x^{2} y + x y^{2} + x^{2} y - x y^{2} + y^{3})$
$\Rightarrow (x^{3} + y^{3})$

L.H.S
Hence, proved.

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