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The factors of the expression 8a³ + b³ + 12a²b + 6ab² are:

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(a + b)(a + b)(a + b)

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

(3a + b)(3a + b)(3a + b)

(4a + b)(4a + b)(4a + b)

answer is B.

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Detailed Solution

Given: 8a³ + b³ + 12a²b + 6ab²
Let us rewrite the given expression as:

8 a 3 + b 3 + 12 a 2 b + 6 a b 2 = (2 a) 3 + b 3 + 3 (2 a) 2 b + 3 (2 a) (b) 2

By using identity, (a + b)³ = a³ + b³ + 3a²b + 3ab², we get

= (2 a + b) 3

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

Hence, 8a³ + b³ + 12a²b + 6ab² = (2a + b)(2a + b)(2a + b)
Therefore, the correct option is 2.

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