Question

What is the middle term in the expansion of (x/2 + 6y)^8?

(a) 45360x^4

(b) 34210x^3

(c) 1207x^4

(d) 3250x^5

The question was posed to me in an online interview.

Asked question is from Counting topic in portion Counting of Discrete Mathematics

Answer 1

The correct choice is (a) 45360x^4

Explanation: We know that in the expansion of (x+y)^n, if n is even then the middle term is (n/2 + 1)^th term. Hence, the middle term in the expansion of (x/2 + 6y)^8 is   (8/2+1)^th = 5^th term.

Now, assuming that x^5 occurs in the (r+1)^th term of the expansion (x/2+6y)^8, we obtain Tr+1 =^nCrx^n-ry^r = ^8C4(x/2)^4(6y)^4 = 45360x^4.