The correct option is A (b+2c)
Given, the expression is
6ab−b2+12ac−2bc(6a−b)
Consider the numerator,
6ab−b2+12ac−2bc6ab=6×a×bb2=b×b
Both the terms have b as a common factor.
12ac=2×2×3×a×c2bc=2×b×c
Both the terms have 2 and c as common factors.
By taking the common factors out,
6ab−b2+12ac−2bc=b(6a−b)+2c(6a−b)
=(b+2c)(6a−b)
So, 6ab−b2+12ac−2bc(6a−b)=(b+2c)(6a−b)(6a−b) =(b+2c)