Factorize:
$(a^{2} - b^{2}) x^{2} + 2 a x + 1$ .

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Solution

Now,
$(a^{2} - b^{2}) x^{2} + 2 a x + 1$
$= (a^{2} x^{2} + 2 a x + 1 - b^{2} x^{2}$
$= (a x + 1)^{2} - (b x)^{2}$
$= (a x + b x + 1) (a x - b x + 1)$ .

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