Factorize the following using the Identities:
$x^{2} - 64$

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Solution

Comparing $x^{2} - 64$ with $a^{2} - b^{2}$ , we see that $a = x$ and $b = 8$
Using, $a^{2} - b^{2} = (a + b) (a - b)$ ,
$x^{2} - 64 = x^{2} - 8^{2}$
$= (x + 8) (x - 8)$
$∴$ The factors of $x^{2} - 64$ are $(x + 8)$ and $(x - 8)$

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