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The factors of the expression 64a³ – 27b³ – 144a²b + 108ab² is:

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(a – 3b)(a – 3b)(a – 3b)

(2a – 3b)(2a – 3b)(2a – 3b)

(3a – 3b)(3a – 3b)(3a – 3b)

(4a – 3b)(4a – 3b)(4a – 3b)

answer is D.

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Detailed Solution

Given: 64a³ – 27b³ – 144a²b + 108ab²
Let us first rewrite the given expression as:

64 a 3 − 27 b 3 − 144 a 2 b + 108 a b 2 = (4 a) 3 − (3 b) 3 − 3 (4 a) 2 (3 b) + 3 (4 a) (3 b) 2

Let us use the identity here:
(a – b)³ = a³ – b³ – 3a²b + 3ab²:

= (4 a − 3 b) 3

= (4 a − 3 b) (4 a − 3 b) (4 a − 3 b)

Hence,64a³ – 27b³ – 144a²b + 108ab² = (4a – 3b)(4a – 3b)(4a – 3b)
Therefore, the correct option is 4.

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