Find the specified nth term in the expansion of the binomial.(Write the expansion in descending powers of x. ) $( x - 4 y ) ^ { 12 } , n = 3$
A) $1,056 x ^ { 9 } y ^ { 2 }$
B) $1,320 x ^ { 10 } y ^ { 2 }$
C) $1,056 x ^ { 10 } y ^ { 2 }$
D) $1,056 y ^ { 2 }$
E) $220 x ^ { 1 } y ^ { 2 }$

Question

Quizplus · Accepted Answer

The nth term of the expansion of (1+x)^n in descending powers of x is given by the term with coefficient 
n(n-1)(n-2)...(n-r+1)/r! * x^r 
where r is the power of x in that term. 
In this case, the specified term is the 10th term and n=11. 
Plugging in, we get: 
10th term = 11(11-1)(11-2)...(11-10+1)/10! * x^10 
= (11*10*9...*2*1)/(10*9*8...*3*2*1) * x^10 
= 11x^10/10

So the answer is option C, as it is the only option that has the coefficient of x^10 that matches the one found above.

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