a) 1

b) 2

c) 3

d) 4

correct answer is: b) 2

Formula use:
a^3+b^3=\left(a+b\right)\left(a^2-ab+b^2\right)
a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)

Explanation

Here, given expression is :
\left(2a+1\right)\left(4a^2-2a+1\right)-\left(2a-1\right)\left(4a^2+2a+1\right)
\rightarrow\left(2a+1\right)\{\left(2a\right)^2-2a.1+\left(1\right)^2\}-\left(2a-1\right)\{\left(2a\right)^2+2a.1+\left(1\right)^2\}
\rightarrow\{\left(2a\right)^3+\left(1\right)^3\}-\{\left(2a\right)^3-\left(1\right)^3\}
\rightarrow\left({8a}^3+1^3-{8a}^3+1^3\right)
\rightarrow\left(1+1\right)
\therefore 2
Ans: 2.