Question

What is the middle term of (x^2 + x)^3?

(a) 3x^4

(b) 6x^4

(c) 4x^4

(d) 3x^6

This question was addressed to me during an online interview.

Asked question is from Binomial Theorem topic in chapter Binomial Theorem of Mathematics – Class 11

Answer 1

Correct choice is (a) 3x^4

Easy explanation: Since the power is odd, there will be even number of terms and two middle terms.

r = \(\frac{n + 1}{2}\) and r = \(\frac{n – 1}{2}\)

Here n = 3

Therefore, r = 2 and r = 1.

When r = 2, ^3C2 (x^2)^3 – 2(x)^2 = 3x^4

When r = 1, ^3C1 (x^2)^3 – 1(x)^1 = 3x^5