Factorize:
$9 c - a^{2} + 4 a - 4 b^{2}$

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Solution

$9 c - a^{2} + 4 a - 4 b^{2} \Rightarrow (9 c - 4 b^{2}) + a (4 - a) \Rightarrow {{(3 \sqrt{c})}^{2} - {(2 b)}^{2}} + a (4 - a) [∵ a^{2} - b^{2} = (a - b) (a + b)] \Rightarrow (3 \sqrt{c} - 2 b) (3 \sqrt{c} + 2 b) + a (4 - a)$

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