Factorise
(2a +1)³ + (a– 1)³

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Solution

(2a +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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