Factorise : $(2 a + b)^{2} + 5 (2 a + b) + 6$

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Solution

$L e t (2 a + b) = x ∴ (2 a + b)^{2} = x^{2} ∴ (2 a + b)^{2} + 5 (2 a + b) + 6 = x^{2} + 5 x + 6 = x^{2} + 3 x + 2 x + 6 = x (x + 3) + 2 (x + 3) = (x + 3) (x + 2) = (2 a + b + 3) (2 a + b + 2) Substituting the value of x$

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