Find coefficients of $x^2$ and $x^3$ in the expansion of $(3 − 2x) ^6$

Question

The coefficients of $x^2$ and $x^3$ in the expansion of $(3 − 2x) ^6$ are $a$ and $b$ respectively. What is the value of $a$ and $b$?

They need to be good at the binomial theorem and know the formulas.

Answer 1

Hint: By binomial theorem $$(3-2x)^6=2^6\sum_{k=0}^6 {6\choose k}\left(\frac{3}{2}\right)^kx^{6-k}.$$