Question

3. Evaluate the coefficients of $x^3$ and $x^4$ in the binomial expansion of $(rac{x}{3} - 3)^7$. Hence evaluate the coefficient of $x^5$ in the expansion of $(rac{x}{3} - 3)^7 (x + 6)$.

          3. Evaluate the coefficients of $x^3$ and $x^4$ in the binomial expansion of $(rac{x}{3} - 3)^7$.
Hence evaluate the coefficient of $x^5$ in the expansion of $(rac{x}{3} - 3)^7 (x + 6)$.

Added by Tammie B.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Nicole Hoffman

06/26/2022

Step 1

The general term is given by: $T_{r+1} = \binom{n}{r} a^{n-r} b^r$, where $n=7$, $a = \frac{x}{3}$, and $b = -3$. So, $T_{r+1} = \binom{7}{r} (\frac{x}{3})^{7-r} (-3)^r = \binom{7}{r} \frac{x^{7-r}}{3^{7-r}} (-3)^r = \binom{7}{r} (-1)^r 3^{r - (7-r)} x^{7-r} = Show more…

Show all steps

Thanks for your feedback!

3. Evaluate the coefficients of $x^3$ and $x^4$ in the binomial expansion of $(\frac{x}{3} - 3)^7$. Hence evaluate the coefficient of $x^5$ in the expansion of $(\frac{x}{3} - 3)^7 (x + 6)$.