Simplify :
$4 a^{2} - b^{2} + 6 b - 9$

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Solution

$4 a^{2} - b^{2} + 6 b - 9$
$= 4 a^{2} - (b^{2} + 9 - 6 b)$
$= 4 a^{2} - (b^{2} + 3^{2} - 2. b .3)$
$= 4 a^{2} - (b - 3)^{2}$
$= (2 a)^{2} - (b - 3)^{2}$
$= (2 a + (b - 3)] [2 a - (b - 3)]$
$= (2 a + b - 3) (2 a - b + 3)$ .

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