Factorise the following polynomial
$9 (2 x - y)^{2} - 4 (2 x - y) - 13$

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Solution

$9 (2 x - y)^{2} - 4 (2 x - y) - 13$

$= 9 (2 x - y)^{2} - 13 (2 x - y) + 9 (2 x - y) - 13$

$= (2 x - y) [9 (2 x - y) - 13] + 1 [9 (2 x - y) - 13]$

$= [9 (2 x - y) - 13] [(2 x - y) + 1]$

$= (18 x - 9 y - 13) (2 x - y + 1)$

Hence factorized.

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