Find the term indicated in the expansion.
-$( x + 3 y ) ^ { 9 } ;$ 4th term
A) $2268 x ^ { 6 } y ^ { 3 }$
B) $756 x ^ { 6 } y ^ { 4 }$
C) $756 x ^ { 3 } y ^ { 6 }$
D) $2268 x ^ { 3 } y ^ { 6 }$

Question

Quizplus · Accepted Answer

The 4th term in the expansion of $(x + 3y)^9$ can be found using the binomial theorem formula for the $k$th term: $_{n}C_{k-1} \cdot x^{n-(k-1)} \cdot y^{k-1}$, where $n=9$ and $k=4$. Thus, the 4th term is $_{9}C_{3} \cdot x^{9-3} \cdot (3y)^{3} = 84 \cdot x^6 \cdot 27y^3 = 2268x^6y^3$.

Find the Term Indicated in the Expansion (x+3y)9;( x + 3 y ) ^ { 9 } ;(x+3y)9;

Find the Term Indicated in the Expansion $( x + 3 y ) ^ { 9 } ;$