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

Question

Quizplus · Accepted Answer

The 10th term in the binomial expansion is given by $\binom{11}{9}\left(\frac{a}{3}\right)^2\left(\frac{-y}{3}\right)^9$. This simplifies to $\frac{55}{177,147}a^2y^9$, which matches choice D. Therefore, the answer is choice D.

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