$6 a b - 216 a^{4} b = (6 a b) (?) (1 + 6 a + 36 a^{2})$

(1 - 6 a)

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(1 + 6 a)

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- 6 a

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6 a^{2}

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Solution

The correct option is C $- 6 a$
$6 a b - 216 a^{4} b = 6 a b (1 - (6 a)^{3})$
We know that the difference of two cubes, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$
So, $6 a b (1 - (6 a)^{3}) = (6 a b) (1 - 6 a) (1^{2} + 6 a + (6 a)^{2})$
$6 a b (1 - (6 a)^{3}) = (6 a b) (1 - 6 a) (1 + 6 a + 36 a^{2})$

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