Find the specified nth term in the expansion of the binomial. $( x - 8 y ) ^ { 5 } , n = 3$
A) $640 x ^ { 5 } y ^ { 3 }$
B) $640 x ^ { 3 } y ^ { 2 }$
C) $640 x ^ { 2 } y ^ { 2 }$
D) $640 x ^ { 3 } y ^ { 3 }$
E) $640 x ^ { 2 } y ^ { 3 }$

Question

Find the specified nth term in the expansion of the binomial.   $( x - 8 y ) ^ { 5 } , n = 3$  
A) $640 x ^ { 5 } y ^ { 3 }$
B) $640 x ^ { 3 } y ^ { 2 }$
C) $640 x ^ { 2 } y ^ { 2 }$
D) $640 x ^ { 3 } y ^ { 3 }$
E) $640 x ^ { 2 } y ^ { 3 }$

Quizplus · Accepted Answer

The nth term in the expansion of $(a + b)^n$ is given by $\binom{n}{k} a^{n-k}b^k$, where $k = n - 1$ for the nth term. For the 3rd term in the expansion of $(x - 8y)^5$, $n = 5$ and $k = 3 - 1 = 2$, so the term is $\binom{5}{2} x^{5-2}(-8y)^2 = 10 \cdot x^3 \cdot 64y^2 = 640x^3y^2$.

Find the Specified Nth Term in the Expansion of the Binomial