Factorise the following expressions
$7 + 10 (2 x - 3 y) - 8 (2 x - 3 y)^{2}$

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Solution

$7 + 10 (2 x - 3 y) - 8 (2 x - 3 y)^{2}$
Let $2 x - 3 y = z$
Then, $7 + 10 (2 x - 3 y) - 8 (2 x - 3 y)^{2}$ becomes
= $7 + 10 z - 8 z^{2}$
= $7 + 14 z - 4 z - 8 z^{2}$
= $7 (1 + 2 z) - 4 z (1 + 2 z)$
= $(1 + 2 z) (7 - 4 z)$
Now, on substituting $z = 2 x - 3 y$ , we get
= $[(1 + 2 (2 x - 3 y))] [7 - 4 (2 x - 3 y)]$
= $(1 + 4 x - 6 y) (7 - 8 x + 12 y)$

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