# What is the general formula for binomial expansion?

## What is the general formula for binomial expansion?

The general term of the binomial expansion is Tr+1=nCrxn−ryr T r + 1 = n C r x n − r y r . Here the coefficient values are found from the pascals triangle or using the combinations formula, and the sum of the exponents of both the terms in the general term is equal to n.

What is expansion formula?

In binomial expansion, a polynomial (x + y)n is expanded into a sum involving terms of the form a x + b y + c, where b and c are non-negative integers, and the coefficient a is a positive integer depending on the value of n and b. …

### What is the binomial expansion rule?

The Binomial theorem tells us how to expand expressions of the form (a+b)ⁿ, for example, (x+y)⁷. The larger the power is, the harder it is to expand expressions like this directly.

How do you start a binomial expansion?

To get started, you need to identify the two terms from your binomial (the x and y positions of our formula above) and the power (n) you are expanding the binomial to. For example, to expand (2x-3)³, the two terms are 2x and -3 and the power, or n value, is 3.

#### What is NCR formula?

The combinations formula is: nCr = n! / ((n – r)! r!) n = the number of items.

What is the formula for the binomial expansion?

Binomial Expansion Formula. The Binomial Expansion Theorem is an algebra formula that describes the algebraic expansion of powers of a binomial. According to the binomial expansion theorem, it is possible to expand any power of x + y into a sum of the form.

## What are the properties of the binomial formula?

The binomial has two properties that can help us to determine the coefficients of the remaining terms. The variables m and n do not have numerical coefficients. So, the given numbers are the outcome of calculating the coefficient formula for each term. The power of the binomial is 9.

Can a power increase with the binomial theorem?

Binomial Theorem – As the power increases the expansion becomes lengthy and tedious to calculate. A binomial expression that has been raised to a very large power can be easily calculated with the help of Binomial Theorem.

### Which is an application of the binomial theorem?

The Binomial Theorem is the method of expanding an expression which has been raised to any finite power. A binomial Theorem is a powerful tool of expansion, which has application in Algebra, probability, etc.