Factorise : a^3 + 3a^2b + 3ab^2 + b^3 - 8 - Vidyadip

Question

Factorise $: a^3 + 3a^2b + 3ab^2 + b^3 - 8$

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Answer

$a^3 + 3a^2b + 3ab^2 + b^3 - 8$
$= (a + b)^3 - 2^3$
$=[(a + b) - 2][(a + b)^2 + (a + b)2 + 2^2]$
$=(a + b - 2)[(a + b)^2 + 2(a + b) + 4]$

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