Find the coefficient $a$ of the term in the expansion of the binomial.
$\begin{array}{ll}
\text { Binomial } & \text { Term } \
(x-3 y)^{6} & a x^{3} y^{3}
\end{array}$

A) $a = 9$
B) $a = - 540$
C) $a = 18$
D) $a = 729$
E) $\quad a = 120$

Question

Find the coefficient $a$ of the term in the expansion of the binomial.
$\begin{array}{ll}
\text { Binomial } & \text { Term } \
(x-3 y)^{6} & a x^{3} y^{3}
\end{array}$

A) $a = 9$
B) $a = - 540$
C) $a = 18$
D) $a = 729$
E) $\quad a = 120$

Quizplus · Accepted Answer

The coefficient $a$ can be found using the binomial theorem, which in this case is $\binom{n}{k} x^{n-k}(-3y)^k$ for the term $x^{n-k}y^k$ in the expansion of $(x-3y)^n$, where $n=6$ and $k=3$. Thus, $a = \binom{6}{3}(-3)^3 = 20 \times -27 = -540$.

Find the Coefficient aaa Of the Term in the Expansion of the Binomial

Find the Coefficient $a$ Of the Term in the Expansion of the Binomial