# How binomial theorem is solved?

## How binomial theorem is solved?

The binomial theorem formula is (a+b)n=∑nr=0(nCr)an−rbr ( a + b ) n = ∑ r = 0 n ( n C r ) a n − r b r , where n is a positive integer and a, b are real numbers and 0 < r ≤ n. This formula helps to expand the binomial expressions such as x + a, (2x + 5)3, (x – (1/x))4, and so on.

### How is binomial theorem used in real life?

Real-world use of Binomial Theorem: The binomial theorem is used heavily in Statistical and Probability Analyses. It is so much useful as our economy depends on Statistical and Probability Analyses. In higher mathematics and calculation, the Binomial Theorem is used in finding roots of equations in higher powers.

What does binomial coefficient mean in statistics?

The binomial coefficient is the number of ways of picking unordered outcomes from possibilities, also known as a combination or combinatorial number.

How do you find 5 c2?

Solution. In both of our solving processes, we see that 5 C 2 = 10. In other words, there are 10 possible combinations of 2 objects chosen from 5 objects.

## What is the coefficient of a binomial?

Also, the coefficient of x is 1, the exponent of x is 1 and 2 is the constant here. Therefore, A binomial is a two-term algebraic expression that contains variable, coefficient, exponents and constant.

### Which is an example of a binomial power?

For example a + b, 2x– y3 etc. The algebraic expansion of binomial powers is described by the binomial theorem, which use Pascal’s triangles to calculate coefficients. The Binomial Theorem states that for a non-negative integer n,

What do the exclamation points mean in a binomial coefficient formula?

Formula for Binomial Coefficients. The exclamation points are actually part of the formula (and they don’t mean the numbers are excited). The notation n! is called the factorial of n, and it means to multiply n times ( n – 1) times ( n – 2), times every whole number down to 1. For example, 5! = 5 * 4 * 3 * 2 * 1 = 120.

How do you find the binomial theorem formula?

Binomial Theorem Formula. If you want to expand a binomial expression with some higher power, then Binomial theorem formula works well for it. Following is the Binomial theorem formula: (x + y)n = Σr=0n nCr xn – r · yr. where, n C r = n!⁄ (n-r)!r! Where n! Denotes the product of all the whole numbers between 1 to n.