Binomial Theorem Calculator

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A binomial is a polynomial with only two terms and Binomial theorem explains the result when a binomial is multiplied as many times by itself. With the help of the Binomial theorem, we can get the termsof any binomial with any degree. Binomial theorem calculator is an instant and fun tool useful in finding the answer easily.

Example 1: Using the Binomial theorem, find the tenth term in the expansion,
(x + 2)12
 
Binomial Theorem expansion formula: (a+b)n = ∑nk=0 (nkC) * an-k * bk

For (x + 2)12 a = x, b = 2, n = 12

Since we need the 10th term in the expansion, hence k = 10 - 1 = 9

(nkC) * an-k * bk = (129C) * x12-9 * 29

129C = (12!)/ [(12-9)!*(9!)
 
129C= (12!)/ (3!*9!)=220
 
(nkC) * an-k * bk = (129C) * x12-9 * 29 = 220*x3*512  = 112640x3



Example 2:Using the Binomial theorem, find the third term in the expansion,
(x + 3)6
 
Binomial Theorem expansion formula: (a+b)n = ∑nk=0 (nkC)* an-k*bk

For (x + 3)a = x,b = 3, n = 6

Since we need the 3rdterm in the expansion, hence k=3-1=2

(nkC) * an-k * bk = (62C) * x6-2 * 32

62C = (6!)/ [(6-2)!*(2!)
 
62C= (6!)/ (4!*2!)= 15
 
(nkC) * an-k * bk = (62C) * x6-2 * 32 =15 *x4 * 9 = 135x4



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