Factorise: $(2 a + 3 b)^{2} - 5 (2 a + 3 b) - 14$

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Solution

$(2 a + 3 b)^{2} - 5 (2 a + 3 b) - 14$
Let $2 a + 3 b = x$
$x^{2} - 5 x - 14$
$x^{2} + 2 x - 7 x - 14$
$x (x + 2) - 7 (x + 2)$
$(x - 7) (x + 2)$
Substitute x with " $2 a + 3 b$ "
$(2 a + 3 b - 7) (2 a + 3 b + 2)$

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