#### A PHP Error was encountered

Severity: Warning

Message: count(): Parameter must be an array or an object that implements Countable

Filename: controllers/calculator.php

Line Number: 37

Binomial Theorem Calculator - Online Calculator - Tutorpace

# Binomial Theorem Calculator

## Online Tutoring Is The Easiest, Most Cost-Effective Way For Students To Get The Help They Need Whenever They Need It.

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