If $a + b = 10$ and $a b = 21$ , find the value of $a^{3} + b^{3}$

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Solution

$a^{3} + b^{3} = (a + b) (a^{2} + b^{2} - a b)$
$= (a + b) [(a + b)^{2} - 3 a b]$
$= 10 [100 - 63]$
$= 10 (37) = 370$

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a + b = 10

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If a - b = 4 and ab = 21, find the value of $a^{3} - b^{3} .$

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