Find the term independent of x in the expansion of : (3x^2/2 - 1/3x)^6

Question

Find the term independent of x in the expansion of : \(\Big(\frac{3x^2}{2} - \frac{1}{3x}\Big)^6\)

Answer 1

To Find : term independent of x, i.e. x⁰

For \(\Big(\frac{3x^2}{2} - \frac{1}{3x}\Big)^6\)

\(a=\frac{3x^2}{2},b= - \frac{1}{3x}\) and n=6 

We have a formula,

Now, to get coefficient of term independent of x that is coefficient of x⁰ we must have, 

(x)^12-3r = x⁰ 

• 12 - 3r = 0 

• 3r = 12 

• r = 4

Therefore, coefficient of x⁰

Conclusion : coefficient of x⁰ = \(\frac{15}{36}\)