Find the coefficient a of the term in the expansion of the binomial. $\begin{array}{lr}\text { Binominal }&\text { Terms }\
(2 x-5 y)^{9} &a x^{4} y^{5}
\end{array}$

A)-6,300,001
B)-6,300,002
C)-6,299,999
D)-6,300,000
E)-6,299,997

Question

Find the coefficient a of the term in the expansion of the binomial. $\begin{array}{lr}\text { Binominal }&\text { Terms }\
(2 x-5 y)^{9} &a x^{4} y^{5}
\end{array}$

A)-6,300,001
B)-6,300,002
C)-6,299,999
D)-6,300,000
E)-6,299,997

Quizplus · Accepted Answer

The coefficient $a$ of the term $x^4y^5$ in the expansion of $(2x-5y)^9$ can be found using the binomial theorem. The general term in the expansion of $(a+b)^n$ is given by $\binom{n}{k}a^{n-k}b^k$, where $\binom{n}{k}$ is the binomial coefficient. For the term $x^4y^5$, $n=9$, $k=5$, $a=2x$, and $b=-5y$. Thus, the coefficient is $\binom{9}{5}(2)^4(-5)^5 = 126 \cdot 16 \cdot -3125 = -6,300,000$.

Find the Coefficient a of the Term in the Expansion Binominal Terms (2x−5y)9ax4y5\begin{array}{lr}\text { Binominal }&\text { Terms }\\(2 x-5 y)^{9} &a x^{4} y^{5}\end{array} Binominal (2x−5y)9​ Terms ax4y5​

Find the Coefficient a of the Term in the Expansion $\begin{array}{lr}\text { Binominal }&\text { Terms }\\(2 x-5 y)^{9} &a x^{4} y^{5}\end{array}$