Factorise $(2 x - y)^{2} - 14 x + 7 y - 18$

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Solution

Given $(2 x - y)^{2} - 14 x + 7 y - 18$
Taking 7 common in the middle terms , we get
$\to$ $(2 x - y)^{2} - 7 (2 x - y) - 18$
Let $2 x - y = a$
$\to$ $a^{2} - 7 a - 18$
Using splitting the middle term , we get
$\to$ $a^{2} - 9 a + 2 a - 18$
$\to$ $a (a - 9) - 2 (a - 9)$
Taking (a-9) as common bracket , we get
$\to$ $(a - 9) (a - 2)$
Re-substituting for a , we get
$\to$ $(2 x - y - 9) (2 x - y - 2)$

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