Find the 10th term in the binomial expansion. $$\left( \frac { z } { 3 } - \frac { d } { 3 } \right) ^ { 11 }$$
A) $\quad - \frac { 11 } { 177,147 } z ^ { 2 } d ^ { 9 }$
B) $\quad - \frac { 55 } { 177,147 } z ^ { 2 } d ^ { 9 }$
C) $\quad - \frac { 1 } { 24 } z d ^ { 10 }$
D) $\quad \frac { 55 } { 128 } z ^ { 2 } d ^ { 9 }$
E) none of the above

Question

Quizplus · Accepted Answer

The 10th term in the binomial expansion of $(a+b)^n$ is ${n\choose 9}a^{n-9}b^9$.
In this case, we have $a=\frac{z}{3}$ and $b=-\frac{d}{3}$, so the 10th term in the expansion is ${11\choose9}\left(\frac{z}{3}\right)^2\left(-\frac{d}{3}\right)^9=-\frac{55}{177,147}z^2d^9$. Therefore, the answer is (B).

Find the 10th Term in the Binomial Expansion (z3−d3)11\left( \frac { z } { 3 } - \frac { d } { 3 } \right) ^ { 11 }(3z​−3d​)11

Find the 10th Term in the Binomial Expansion $\left( \frac { z } { 3 } - \frac { d } { 3 } \right) ^ { 11 }$