Expanding: (a+b)^3 (a b)^3 = (2b)((a+b)^2 +(a b)^2 + (a+b)(a b) ) =(2b)(3a^2 b^2) =(2b)(√(3)a +b)(√( ...

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Algebraic Identities

Factorise a+b...

Question

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

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Solution

Expanding:

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

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

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

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