Find the HCF of $6 (a^{2} - b^{2}), 21 (a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3})$ , and $15 (a^{2} + 2 a b + b^{2})$

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Solution

The $H C F$ of $6, 21,$ and $15$ is $3$ .
$a^{2} - b^{2} = (a + b) (a - b)$
$a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3} = (a - b)^{3}$
$a^{2} + 2 a b + b^{2} = (a + b)^{2}$
Lowest power of $(a + b) = (a + b)$
Lowest power of $(a - b) = (a - b)$
$∴ H C F = 3 (a + b) (a - b)$

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