Find the coefficient of the given term in the binomial expansion.
-$x ^ { 6 }$ term, $( x - 3 ) ^ { 15 }$
A) $- 15,015$
B) $98,513,415$
C) $- 98,513,415$
D) 5005

Question

Quizplus · Accepted Answer

The coefficient of $x^6$ in the expansion of $(x - 3)^{15}$ can be found using the binomial theorem, specifically the term is given by $\binom{n}{k}a^{n-k}b^k$ where $n=15$, $k=6$, $a=x$, and $b=-3$. Thus, the coefficient is $\binom{15}{6}(-3)^{6} = 5005 \times 729 = -3,645,135$. However, none of the provided options match this calculation, indicating a mistake in my initial explanation. Correcting this, the coefficient for the $x^6$ term actually involves calculating $\binom{15}{6}(-3)^{9}$, leading to the correct coefficient of $-98,513,415$, as negative signs and powers were initially miscalculated.

Find the Coefficient of the Given Term in the Binomial x6x ^ { 6 }x6

Find the Coefficient of the Given Term in the Binomial $x ^ { 6 }$