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A day full of math games & activities. Find one near you.
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 ,
Tr + 1 = \(^nC_{r} a^{n-r} b^r\)
So, (a + b)6,
n = 6
By substituting the values we get,
T3 = T2 + 1 = \(^6C_{2} a^{6-2} b^2\)
= (6!/(4!2!))a4b2
= 3 × 5a4b2
= 15a4b2
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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