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Algebraic Identities

Factorise: 2a...

Question

Factorise:
$(2 a + 1)^{3} + (a - 1)^{3}$

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Solution

$(2 a + 1)^{3} + (a - 1)^{3} = (2 a + 1 + a - 1) ((2 a + 1)^{2} + (a - 1)^{2} - (2 a + 1) (a - 1)) = (3 a) (4 a^{2} + 1 + 4 a + a^{2} + 1 - 2 a - 2 a^{2} + 2 a - a + 1) = (3 a) (3 a^{2} + 3 a + 3) = (9 a) (a^{2} + a + 1)$

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