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,

T₃ = T_{2 + 1} = \(^6C_{2} a^{6-2} b^2\)

= (6!/(4!2!))a⁴b²

= 3 × 5a⁴b²

= 15a⁴b²

Therefore, the coefficient of the third term is 15.

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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.