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

(2 a - b)^{2}

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(2 a - b)^{3}

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(a - b)^{3}

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(2 a + b)^{3}

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Solution

The correct option is C $(2 a - b)^{3}$
$8 a^{3} - b^{3} - 12 a^{2} b + 6 a b^{2}$
$= {(2 a)}^{3} - b^{3} - 6 a b (2 a - b)$
$= {(2 a)}^{3} - b^{3} - 3 \times (2 a) (b) (2 a - b)$
$= {(2 a - b)}^{3}$
Hence, the answer is ${(2 a - b)}^{3} .$

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Similar questions

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

(2 a + b)^{3}

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

Factorise : 8a³ + b³ + 12a²b + 6ab²

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

= (2 a + b) (2 a + b) (2 a + b)

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

= (2 a - b) (2 a - b) (2 a - b)

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