Find the specified nth term in the expansion of the binomial. $( 4 x + 3 y ) ^ { 9 } , n = 8$
A) $1,259,712 x ^ { 7 } y ^ { 2 }$
B) $1,259,712 x ^ { 2 } y ^ { 7 }$
C) $1,259,712 x ^ { 8 } y ^ { 9 }$
D) $1,259,712 x ^ { 2 } y ^ { 2 }$
E) $1,259,712 x ^ { 7 } y ^ { 7 }$

Question

Find the specified nth term in the expansion of the binomial.​ $( 4 x + 3 y ) ^ { 9 } , n = 8$ ​
A) $1,259,712 x ^ { 7 } y ^ { 2 }$
B) $1,259,712 x ^ { 2 } y ^ { 7 }$
C) $1,259,712 x ^ { 8 } y ^ { 9 }$
D) $1,259,712 x ^ { 2 } y ^ { 2 }$
E) $1,259,712 x ^ { 7 } y ^ { 7 }$

Quizplus · Accepted Answer

The coefficient of the nth term in the expansion of (a+b)^n is given by the binomial coefficient (n choose k), where k is the index of the term (starting from 0). In this case, n=11 and k=5825, so the binomial coefficient is (11 choose 5825). This is equivalent to choosing 5825 objects out of 11, which is obviously not possible, but the binomial coefficient is defined as 0 in such cases. Therefore, the nth term is simply b^(11-5825)*a^5825, which equals b^5825*a^(-5814). This can be seen in choice B, where the coefficients of a and b match this expression.

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

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