Find the term indicated in the expansion.
-$( x + 2 y ) ^ { 12 }$; 11th term
A) $67,584 x ^ { 2 } y ^ { 10 }$
B) $33,792 x ^ { 2 } y^{ 11}$
C) $33,792 \mathrm { x } 10 \mathrm { y } ^2$
D) $67,584 \mathrm { x } 10 \mathrm { y }^ 2$

Question

Quizplus · Accepted Answer

The 11th term in the expansion of $(x + 2y)^{12}$ can be found using the binomial theorem formula for the $k$th term: $T_{k} = \binom{n}{k-1} \cdot x^{n-(k-1)} \cdot (2y)^{k-1}$, where $n = 12$ and $k = 11$. Thus, $T_{11} = \binom{12}{10} \cdot x^{12-10} \cdot (2y)^{10} = 66 \cdot x^2 \cdot (2^{10}y^{10}) = 67,584 x^2 y^{10}$.

Find the Term Indicated in the Expansion (x+2y)12( x + 2 y ) ^ { 12 }(x+2y)12

Find the Term Indicated in the Expansion $( x + 2 y ) ^ { 12 }$