Factorize :
$a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3} - 8$

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Solution

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

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Similar questions

a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3} - 8

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

Which of the following is an expansion of the identity ${(a - b)}^{3}$ ?

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

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