Find the indicated term of the binomial expansion.
-$\left( 2 r + s ^ { 2 } \right) ^ { 10 }$; eighth term
A) $180 r ^ { 2 } s ^ { 16 }$
B) $90 r ^ { 2 } s ^ { 8 }$
C) $960 r ^ { 3 } s ^ { 14 }$
D) $240 r ^ { 3 } s ^ { 7 }$

Question

Quizplus · Accepted Answer

The eighth term of the binomial expansion $(a + b)^n$ can be found using the formula for the $k$th term: $T_k = \binom{n}{k-1} a^{n-(k-1)} b^{k-1}$. For the eighth term ($k = 8$) of $(2r + s^2)^{10}$, we use $a = 2r$, $b = s^2$, and $n = 10$. Thus, $T_8 = \binom{10}{7} (2r)^{10-7} (s^2)^7 = \binom{10}{7} (2r)^3 (s^2)^7 = 120 \cdot 8r^3 s^{14} = 960r^3s^{14}$.

Find the Indicated Term of the Binomial Expansion (2r+s2)10\left( 2 r + s ^ { 2 } \right) ^ { 10 }(2r+s2)10

Find the Indicated Term of the Binomial Expansion $\left( 2 r + s ^ { 2 } \right) ^ { 10 }$