Find the indicated term.
-The third term of the expansion of $( 3 x + 5 ) ^ { 3 }$
A) $450 x$
B) 25
C) $135 x ^ { 2 }$
D) $225 x$

Question

Quizplus · Accepted Answer

The third term of the expansion of $( 3 x + 5 ) ^ { 3 }$ is $225 x$. This can be found using the binomial theorem, which states that the expansion of $( a + b ) ^ { n }$ is given by the sum of the terms ${n \choose k} a ^ { n - k } b ^ { k}$, where $k$ ranges from 0 to $n$. In this case, $n = 3$, $a = 3 x$, and $b = 5$. The third term corresponds to $k = 2$, so we have ${3 \choose 2} ( 3 x ) ^ { 3 - 2 } 5 ^ { 2 } = 3 ( 3 x ) 25 = 225 x$.

Find the Indicated Term (3x+5)3( 3 x + 5 ) ^ { 3 }(3x+5)3

Find the Indicated Term $( 3 x + 5 ) ^ { 3 }$