# What is the coefficient of the third term in the binomial expansion of (a + b)^{6}?

1, 15, 20, 90

**Solution:**

The binomial expansion formulas are used to find the powers of the binomials which cannot be expanded using the algebraic identities.

Given:

Binomial expansion is (a + b)^{6}.

(r +1)^{th} term of (a + b)^{n} is given by ,

T_{r + 1} = \(^nC_{r} a^{n-r} b^r\)

So, (a + b)^{6},

n = 6

By substituting the values we get,

T_{3} = T_{2 + 1} = \(^6C_{2} a^{6-2} b^2\)

= (6!/(4!2!))a^{4}b^{2}

= 3 × 5a^{4}b^{2}

= 15a^{4}b^{2}

Therefore, the coefficient of the third term is 15.

## What is the coefficient of the third term in the binomial expansion of (a + b)^{6}?

**Summary:**

The coefficient of the third term in the binomial expansion of (a + b)^{6} is 15.

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