The factors of 8 a^3+b^3-6 a b+1 are:

MCQ

The factors of $8 a^3+b^3-6 a b+1$ are:

A
$(2 a+b-1)\left(4 a^2+b^2+1-3 a b-2 a\right)$
B
$(2 a-b+1)\left(4 a^2+b^2-4 a b+1-2 a+b\right)$
✓
$(2 a+b+1)\left(4 a^2+b^2+1-2 a b-b-2 a\right)$
D
$(2 a-1+b)\left(4 a^2+1-4 a-b-2 a b\right)$

✓

Answer

Correct option: C.

$(2 a+b+1)\left(4 a^2+b^2+1-2 a b-b-2 a\right)$

We know the identity
$a^3+b^3+c^3-3 a b c=(a+b+c)\left(a^2+b^2+c^2-a b-b c-c a\right)$
So by using identity, we can write given expression as
$(2 a)^3+(b)^3+(1)^3-3(2 a)(b)(1)$
$=(2 a+b+1)\left[(2 a)^2+b^2+1^2-2 a \times b-b \times 1-2 a \times 1\right]$
$=(2 a+b+1)\left(4 a^2+b^2+1-2 a b-b-2 a\right)$
Hence, correct option is $(c).$

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