Find the coefficient of the given term in the binomial expansion.
-$x ^ { 6 } y ^ { 7 }$ term, $( x + y ) ^ { 13 }$
A) $1,235,520$
B) 6
C) 1716
D) 205,920

Question

Quizplus · Accepted Answer

The coefficient of the $x^6y^7$ term in the expansion of $(x + y)^{13}$ can be found using the binomial theorem, specifically the binomial coefficient formula $\binom{n}{k} = \frac{n!}{k!(n-k)!}$, where $n$ is the power of the binomial and $k$ is the term number. For the $x^6y^7$ term, $n=13$ and $k=6$ (or equivalently $k=7$, since it's symmetrical), so the coefficient is $\binom{13}{6} = \frac{13!}{6!7!} = 1716$.

Find the Coefficient of the Given Term in the Binomial x6y7x ^ { 6 } y ^ { 7 }x6y7

Find the Coefficient of the Given Term in the Binomial $x ^ { 6 } y ^ { 7 }$