Factorize the following using the Identities:
$x^{2} - 10 x + 25$

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Solution

$x^{2} - 10 x + 25$
Comparing $x^{2} - 10 x + 25$ with $a^{2} - 2 a b + b^{2}$ , we see that $a = x, b = 5$ .
Now, $x^{2} - 10 x + 25 = x^{2} - 2 (x) (5) + 5^{2}$
Using, $a^{2} - 2 a b + b^{2} = (a - b)^{2}, a = x$ and $b = 5$ ,
we get $x^{2} - 10 x + 25 = (x - 5)^{2}$
$∴$ The factors of $x^{2} - 10 x + 25$ are $(x - 5)$ and $(x - 5)$

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