Factorise:

$a (a + b)^{3} - 3 a^{2} b (a + b)$

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Solution

$a (a + b)^{3} - 3 a^{2} b (a + b) = a (a + b) {(a + b)^{2} - 3 a b} = a (a + b) {a^{2} + b^{2} + 2 a b - 3 a b} = a (a + b) (a^{2} - a b + b^{2})$

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a^{3}

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