Find the specified nth term in the expansion of the binomial. $( 4 a + 5 b ) ^ { 5 } , n = 5$
A) $12,500 a b ^ { 4 }$
B) $12,500 a b$
C) $12,500 a ^ { 4 } b$
D) $12,500 a ^ { 4 } b ^ { 4 }$
E) $12,500 a ^ { 5 } b ^ { 5 }$

Question

Find the specified nth term in the expansion of the binomial.​ $( 4 a + 5 b ) ^ { 5 } , n = 5$ ​
A) $12,500 a b ^ { 4 }$
B) $12,500 a b$
C) $12,500 a ^ { 4 } b$
D) $12,500 a ^ { 4 } b ^ { 4 }$
E) $12,500 a ^ { 5 } b ^ { 5 }$

Quizplus · Accepted Answer

The nth term in the binomial expansion is given by $ T_{n+1} = \binom{5}{n} (4a)^{5-n} (5b)^n $. For $ n = 4 $, the term is $ \binom{5}{4} (4a)^{1} (5b)^4 = 5 \times 4a \times 625b^4 = 12,500ab^4 $.

Find the Specified Nth Term in the Expansion of the Binomial.​

Find the Specified Nth Term in the Expansion of the Binomial.