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The factors of the expression 27 – 125a³ – 135a + 225a² is:

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3 – 6a)(3 – 5a)(3 – 5a)

3 – 5a)(3 – 4a)(3 – 5a)

3 – 5a)(3 – 5a)(3 – 6a)

3 – 5a)(3 – 5a)(3 – 5a)

answer is D.

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Detailed Solution

Given: 27 – 125a³ – 135a + 225a².
Now, we shall rewrite the given expression as :

27 − 125 a 3 − 135 a + 225 a 2 = 33 − (5 a) 3 − 3 (3) 2 (5 a) + 3 (3) (5 a) 2

Let us use the identity (a – b)³ = a³ – b³ – 3a²b + 3ab².
Therefore,

27 − 125 a 3 − 135 a + 225 a 2 = (3 − 5 a) 3

= (3 − 5 a) (3 − 5 a) (3 − 5 a)

Hence, 27 – 125a³ – 135a + 225a² = (3 – 5a)(3 – 5a)(3 – 5a).
Therefore, the factors of 27 – 125a³ – 135a + 225a² is (3 – 5a)(3 – 5a)(3 – 5a).
Therefore, the correct option is 4.

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