Find the term indicated in the expansion.
-$( x - 2 y ) ^ { 11 } ; 8$ th term
A) $- 42,240 x ^ { 4 } y ^ { 7 }$
B) $21,120 \mathrm { x } ^ { 4 } \mathrm { y } 8$
C) $21,120 x^ 7 y^ 4$
D) $- 42,240 x ^ { 7 } y ^ { 4 }$

Question

Quizplus · Accepted Answer

The 8th term in the expansion of $(x - 2y)^{11}$ can be found using the binomial theorem formula for the $n$th term: $T_{k+1} = \binom{n}{k} x^{n-k} y^k$, where $n = 11$ and $k = 8 - 1 = 7$. Thus, $T_8 = \binom{11}{7} x^{11-7} (-2y)^7 = \binom{11}{7} x^4 (-2)^7 y^7$. Calculating $\binom{11}{7} = 330$ and $(-2)^7 = -128$, the term becomes $-42,240 x^4 y^7$.

Find the Term Indicated in the Expansion (x−2y)11;8( x - 2 y ) ^ { 11 } ; 8(x−2y)11;8

Find the Term Indicated in the Expansion $( x - 2 y ) ^ { 11 } ; 8$