a) 27q^3

b) 343q^3

c) 1331q^3

d) 3375q^3

correct answer is: a) 27q^3

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

Explanation

Here, given expression is :
\left(3p+2q\right)^3-{3.\left(3p+2q\right)}^2\ \left(3p-q\right)+3\left(3p+2q\right)\left(3p-q\right)^2-\left(3p-q\right)^3
Let,
\left(3p+2q\right)=a
\left(3p-q\right)=b
Now, Simplify the expression :
\left(3p+2q\right)^3-{3.\left(3p+2q\right)}^2\ \left(3p-q\right)+3\left(3p+2q\right)\left(3p-q\right)^2-\left(3p-q\right)^3
\rightarrow a^3-3.a^2.b+3.a.b^2-b^3
\therefore\left(a-b\right)^3
Now putting the value of ‘a’ & ‘b’, we get :
\{\left(3p+2q\right)-\left(3p-q\right)\}^3
\rightarrow\left(3p+2q-3p+q\right)^3
\rightarrow\left(3q\right)^3
\therefore 27q^3
Ans: 27q^3\ .