Factorize: $8 (a - 2 b)^{2} - 2 a + 4 b - 1$ .

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Solution

$8 (a - 2 b)^{2} - 2 a + 4 b - 1$
$\Rightarrow 8 (a - b)^{2} - 2 (a - 2 b) - 1$
$\Rightarrow$ Take $a - 2 b = x$
$∴ 8 x^{2} - 2 x - 1$
$\Rightarrow 8 x^{2} - 4 x + 2 x - 1$
$\Rightarrow 4 x (2 x - 1) + 1 (2 x - 1)$
$\Rightarrow (4 x + 1) (2 x - 1)$
$∴ (4 (a - 2 b) + 1) (2 (a - 2 b) - 1)$
$\Rightarrow (4 a - 8 b + 1) (2 a - 4 b - 1)$ .

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