State True or False.
$64 a^{3} - 27 b^{3} - 144 a^{2} b + 108 a b^{2}$ $= (4 a - 3 b) (4 a - 3 b) (4 a - 3 b)$

True

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False

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Solution

The correct option is A True
We have, $64 a^{3} - 27 b^{3} - 144 a^{2} b + 108 a b^{2} = (4 a)^{3} + (- 3 b)^{3} - 36 a b (4 a - 3 b)$
Using, $(a + b)^{3} = a^{3} + b^{3} + 3 a b (a + b)$
$= (4 a)^{3} + (- 3 b)^{3} + 3 (4 a) (- 3 b) (4 a - 3 b)$
$= (4 a - 3 b)^{3}$
$= (4 a - 3 b) (4 a - 3 b) (4 a - 3 b)$

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Similar questions

64 a^{3} - 27 b^{3} - 144 a^{2} b + 108 a b^{2}

64 a^{3} - 27 b^{3} - 144 a^{2} b + 108 a b^{2}

64 a^{3}

- 27 b^{3}

- 144 a^{2} b

+ 108 a b^{2}

64 a^{3} - 27 b^{3} - 144 a^{2} b + 108 a b^{2}

Factorise each of the following: 64 $a^{3}$ – 27 $b^{3}$ – 144 $a^{2}$ b + 108a $b^{2}$

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