Factorise the following polynomial.
$8 a^{3} + b^{3} + 12 a^{2} b + 6 a b^{2}$

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Solution

Given,
$8 a^{3} + b^{3} + 12 a^{2} b + 6 a b^{2}$
$= (2 a)^{3} + 3 (2 a)^{2} (b) + 3 (2 a) (b)^{2} + (b)^{3}$

This is in the form of $x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3}$ which is equal to $(x + y)^{3}$

where $x = 2 a, y = b$

So, $8 a^{3} + b^{3} + 12 a^{2} b + 6 a b^{2} = (2 a + b)^{3} = (2 a + b) (2 a + b) (2 a + b)$

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Similar questions

8 a^{3} - b^{3} - 12 a^{2} b + 6 a b^{2}

8 a^{3} - b^{3} - 12 a^{2} b + 6 a b^{2}

Factorise : 8a³ + b³ + 12a²b + 6ab²

8 a^{3} + b^{3} + 12 a^{2} b + 6 a b^{2}

Factorise: $8 a^{3} - b^{3} - 12 a^{2} b + 6 a b^{2}$

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