Find the indicated term of the binomial expansion.
-$\left( x ^ { 3 } - 2 y ^ { 2 } \right) ^ { 14 }$; Find the term containing $x ^ { 33 }$.
A) $- 2,912 x ^ { 33 } y ^ { 6 }$
B) $- 2,002 x ^ { 30 } y ^ { 8 }$
C) $- 728 x ^ { 33 } y ^ { 6 }$
D) $- 16,016 x ^ { 30 } y ^ { 8 }$

Question

Quizplus · Accepted Answer

The term containing $x^{33}$ in the expansion of $\left(x^3 - 2y^2\right)^{14}$ can be found using the binomial theorem. The general term in the expansion is given by $\binom{n}{k} (x^3)^{n-k} (-2y^2)^k$, where $n=14$ and $k$ is the term number. To find the term containing $x^{33}$, we set $3(n-k) = 33$, solving for $k$ gives $k = 3$. Substituting $n=14$ and $k=3$ into the general term formula and simplifying gives the coefficient as $-2,912$, making the term $-2,912 x^{33} y^6$.

Find the Indicated Term of the Binomial Expansion (x3−2y2)14\left( x ^ { 3 } - 2 y ^ { 2 } \right) ^ { 14 }(x3−2y2)14

Find the Indicated Term of the Binomial Expansion $\left( x ^ { 3 } - 2 y ^ { 2 } \right) ^ { 14 }$