Factorise : $8 + 6 (a + b) - 5 (a + b)^{2}$

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Solution

$L e t a + b = x ∴ (a + b)^{2} = x^{2} ∴ 8 + 6 (a + b) - 5 (a + b)^{2} = 8 + 6 x - 5 x^{2} = 8 + 10 x - 4 x - 5 x^{2} = 2 (4 + 5 x) - x (4 + 5 x) = (4 + 5 x) (2 - x) = [4 + 5 (a + b)] [2 - (a + b)] Substituting the value of x = [4 + 5 a + 5 b] [2 - a - b]$

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