The factors of `8a^3+b^3-6a b+1` are (a) `(2a+b-1)(4a^2+b^2+1-3a b-2a)` (b)`(2a-b+1)(4a^2+b^2-4a b+1-2a+b)` (c)`(2a+b+1)(4a^2+b^2+1-2a b-b-2a)` (d)`(2a-1+b)(4a^2+1-4a-b-2a b)`

Explanation

`8a^3+b^3-6a b+1`
`= 8a^3+b^3-(3xx2axxbxx1)+1^3`
`=(2a)^3+b^3+1^3-(3xx2axxbxx1)`...`{by,x^3+y^3+z^3-3xyz}`
`=(2a+b+1)\((2a)^2+b^2+1^2-2ab-b-2a)`
`=(2a+b+1)\(4a^2+b^2+1-2ab-b-2a)`
Hence,the factors of
`8a^3+b^3-6a b+1` are
`(2a+b+1)\(4a^2+b^2+1-2ab-b-2a)`.
Therefore ,option C is correct.