Write the indicated term of the binomial expansion.
-$( x + 2 y ) ^ { 12 ; } 4$ th term
A) $1760 x ^ { 3 } y ^ { 9 }$
B) $1760 \mathrm { x } ^ { 9 } \mathrm { y } ^ { 3 }$
C) $880 \mathrm { x } ^ { 9 } \mathrm { y } ^ { 4 }$
D) $880 \mathrm { x } ^ { 3 } \mathrm { y } ^ { 9 }$

Question

Quizplus · Accepted Answer

The 4th term in the expansion of $(x + 2y)^{12}$ can be found using the binomial theorem formula for the $k$th term: $\binom{n}{k-1} \cdot x^{n-(k-1)} \cdot (2y)^{k-1}$, where $n=12$ and $k=4$. This results in $\binom{12}{3} \cdot x^{9} \cdot (2y)^{3}$, simplifying to $220 \cdot x^{9} \cdot 8y^{3} = 1760x^{9}y^{3}$.

Write the Indicated Term of the Binomial Expansion (x+2y)12;4( x + 2 y ) ^ { 12 ; } 4(x+2y)12;4

Write the Indicated Term of the Binomial Expansion $( x + 2 y ) ^ { 12 ; } 4$