Find the 10th term in the binomial expansion. $$\left( \frac { x } { 2 } - \frac { d } { 2 } \right) ^ { 11 }$$
A) $\quad - \frac { 1 } { 24 } x d ^ { 10 }$
B) $\quad - \frac { 55 } { 2,048 } x ^ { 2 } d ^ { 9 }$
C) $\quad \frac { 55 } { 128 } x ^ { 2 } d ^ { 9 }$
D) $\quad - \frac { 11 } { 2,048 } x ^ { 2 } d ^ { 9 }$
E) none of the above

Question

Quizplus · Accepted Answer

The 10th term in the binomial expansion is given by the formula $\binom{11}{9} \left(\frac{x}{2}\right)^2 \left(-\frac{d}{2}\right)^9$. Calculating this gives $-\frac{55}{2048} x^2 d^9$, which matches option B.

Find the 10th Term in the Binomial Expansion (x2−d2)11\left( \frac { x } { 2 } - \frac { d } { 2 } \right) ^ { 11 }(2x​−2d​)11

Find the 10th Term in the Binomial Expansion $\left( \frac { x } { 2 } - \frac { d } { 2 } \right) ^ { 11 }$