(a+2b)^2 a^2=(a+2b)^2 (a)^2 =(a+2b+a)(a+2b a) =(2a+2b)(2b) =2(a+b)(2b) =2× 2b(a+b) =4b(a+b) ...

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Factorisation Using Algebraic Identities

a+2b2-a2

Question

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

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Solution

$(a + 2 b)^{2} - a^{2} = (a + 2 b)^{2} - (a)^{2} = (a + 2 b + a) (a + 2 b - a) = (2 a + 2 b) (2 b) = 2 (a + b) (2 b) = 2 \times 2 b (a + b) = 4 b (a + b)$

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