If $a - b = 4$ and $a b = 45$ , find the value of $a^{3} - b^{3}$ .

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Solution

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

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

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

$a^{3} - b^{3} = 4 \times (4^{2} + 3 \times 45) = 4 \times (16 + 135) = 4 \times 151 = 604$

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