Find the coefficient a of the term in the expansion of the binomial. Binomial Terms
$( 6 x - y ) ^ { 10 }~ a x ^ { 2 } y ^ { 8 }$
A)1,621
B)1,620
C)1,619
D)1,623
E)1,618

Question

Find the coefficient a of the term in the expansion of the binomial.​ Binomial Terms
$( 6 x - y ) ^ { 10 }~ a x ^ { 2 } y ^ { 8 }$ ​
A)1,621
B)1,620
C)1,619
D)1,623
E)1,618

Quizplus · Accepted Answer

The coefficient of the term in the expansion of binomial (a+b)^n is given by the formula,
Coefficient = nCk = n!/(k!(n-k)!)
Here, n=11, k=4 and a=99ea99db-b282-b7c7-94ac-6b611b87522b_TB4590_11
So, the coefficient is 11!/[(99ea99db-b282-b7c7-94ac-6b611b87522b_TB4590_11)!(11-99ea99db-b282-b7c7-94ac-6b611b87522b_TB4590_11)!]
Simplifying this, we get the coefficient as 1,620. Therefore, the answer is B.

Find the Coefficient a of the Term in the Expansion (6x−y)10 ax2y8( 6 x - y ) ^ { 10 }~ a x ^ { 2 } y ^ { 8 }(6x−y)10 ax2y8

Find the Coefficient a of the Term in the Expansion $( 6 x - y ) ^ { 10 }~ a x ^ { 2 } y ^ { 8 }$