factorise
$x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3} - 8$

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Solution

$x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3} - 8$
${x + y)}^{3} - 8$
${(x + y)}^{3} - 2^{3}$
$(x + y - 2) {{(x + y)}^{2} + 2 (x + y) + 2^{2}} (x + y - 2) (x^{2} + y^{2} + 2 x + 2 y + 4 + x y)$

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