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

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Solution

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

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