# What is the third term in the expansion of (x + 2)^{6}?

**Solution:**

Given (x + 2)^{6}

We use binomial theorem to get the expansion

(a + b)^{n} = ∑(k = 0 to n) ^{n}C_{k} (a_{n - k }× b^{k})

Here, a = x and b = 2, n = 6

(x + 2)^{6} = ∑(k=0 to n) ^{6}C_{k} (x)^{6 - k }× (2)^{k}

(x + 2)^{6} = 6! /6!0! (x)^{6}(2)^{0} + 6!/(6 - 1)!1! (x)^{5}(2)^{1} + 6!/(6 - 2)!2! (x)^{4}(2)^{2} + 6!/(6 - 3)!3! (x)^{3}(2)^{3} + 6!/(6 - 4)!4! (x)^{2}(2)^{4} + 6!/(6 - 5)!5! (x)^{1}(2)^{5}

(x + 2)^{6} = 1 × (x)^{6}(2)^{0} + 6 × (x)^{5}(2)^{1} + 15 × x^{4}(2)^{2} + 20x^{3}(2)^{3} + 15 × x^{2}(2)^{4} + 6x^{1}(2)^{5} + 1 × x^{0}(2)^{6}

(x + 2)^{6} = x^{6 }+ 12x^{5 }+ 60x^{4} + 160x^{3} + 240x^{2} + 192x + 64

Coefficient of the third term is 60

## What is the third term in the expansion of (x + 2)^{6}?

**Summary:**

The third term in the expansion of (x + 2)^{6} is 60.

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