Factorize :
$8 (a + 1)^{2} + 2 (a + 1) (b + 2) - 15 (b + 2)^{2}$

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Solution

$8 (a + 1)^{2} + 2 (a + 1) (b + 2) - 15 (b + 2)^{2}$
Let $a + 1 = x$ and $b + 2 = y$ . Then,
$8 x^{2} + 2 x y - 15 y^{2}$
$= 8 x^{2} + 12 x y - 10 x y - 15 y^{2}$
$= 4 x (2 x + 3 y) - 5 y (2 x + 3 y)$
$= (2 x + 3 y) (4 x - 5 y)$
$= (2 a + 3 b + 8) (4 a - 5 b - 6)$

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