Factorise : $4 (2 a + b)^{2} - (a - b)^{2}$

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Solution

$4 (2 a + b)^{2} - (a - b)^{2} = [2 (2 a + b)]^{2} - (a - b)^{2} = [2 (2 a + b) + a - b] [2 (2 a + b) - a + b] = (4 a + 2 b + a - b) (4 a + 2 b - a + b) = (5 a + b) (3 a + 3 b) = (5 a + b) 3 (a + b) = 3 (5 a + b) (a + b)$

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4 (2 a + b)^{2} - (a - b)^{2}

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$9 (2 a - b)^{2} - 4 (2 a - b) - 13$

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