Factorise:

$a^{3} - 27 b^{3} + 2 a^{2} b - 6 a b^{2}$

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Solution

$a^{3} - 27 b^{3} + 2 a^{2} b - 6 a b^{2} \Rightarrow a^{3} - (3 b)^{3} + 2 a b (a - 3 b) \Rightarrow (a - 3 b) (a^{2} + 3 a b + 9 b^{2}) + 2 a b (a - 3 b) \Rightarrow (a - 3 b) (a^{2} + 3 a b + 9 b^{2} + 2 a b) \Rightarrow (a - 3 b) (a^{2} + 5 a b + 9 b^{2})$

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Factorise each of the following:

(i) (ii)

(iii) (iv)

(v)

Factorise:

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a^{3} - 27 b^{3} + 2 a^{2} b - 6 a b^{2}

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