Factorize:

$9 (2 a - b)^{2} - 4 (2 a - b) - 13$

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Solution

$9 (2 a - b)^{2} - 4 (2 a - b) - 13$
Let $2 a - b = x$ , then
$9 x^{2} - 4 x - 13 ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} ∵ 9 \times (- 13) = - 117 - 117 = - 13 \times 9 - 4 = - 13 + 9 \end{matrix} ⎫ ⎪ ⎬ ⎪ ⎭ \Rightarrow 9 x^{2} + 9 x - 13 x - 13 \Rightarrow 9 x (x + 1) - 13 (x + 1) \Rightarrow (x + 1) (9 x - 13) \Rightarrow (2 a - b + 1) {9 (2 a - b) - 13} \Rightarrow (2 a - b + 1) (18 a - 9 b - 13)$

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9 {(2 a - b)}^{2} - 4 (2 a - b) - 13

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