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Created By : Rina Nayak

Reviewed By : Rina Nayak

Last Updated : Apr 17, 2023

Free Handy Binomial Expansion Tool is designed to expand the binomial term in a short span of time. All you have to do provide the binomial term as input and tap on the calculate button to get the result quickly along with the detailed steps

Ex:

Use '^' for exponent

Binomial Expansion of:

### What is Binomial Theorem Expansion?

The binomial theorem is a method that is used to expand an expression that has been raised to a finite power. It has applications in algebra, probability and others. A binomial is a polynomial that has two dissimilar terms. The important points of the binomial expansion are given here. For an expansion of (a + b)n, the total number of terms are (n + 1). The sum of exponents a, b is always n

The formula for the expansion of a binomial defined by binomial theorem is given as:

### Steps to Expand Term Using Binomial Theorem

The step by step process to expand a binomial term is listed here:

1. Get any binomial expression that has a fine power.

2. Substitute the values in the formula of binomial expansion theorem.

3. Solve the question to get the answer.

You can even find various maths free online calculators on our website factorpolynomials.com by just clicking on this link. Make all your complex geometry & algebra calculations quite easy and quick by using our provided calculators.

### Expand Binomial with Example

Example

Question: Expand binomial (x+5)^4.

Solution:

Given binomial is (x + 5)^4

The binomial expansion formula is (a+b)^n = \sum_{k=0}^{n} {^nC_k}(a^{n-k}b^{k}) So (x + 5)^4 = \sum_{k=0}^4 {^4C_k}((x)^{4-k}(5)^{k})

By expanding the summation:

\frac{4!}{(4-0)!0!}(x)^{4-0}\times{}(5)^0+\frac{4!}{(4-1)!1!}(x)^{4-1}\times{}(5)^1+\frac{4!}{(4-2)!2!}(x)^{4-2}\times{}(5)^2+\frac{4!}{(4-3)!3!}(x)^{4-3}\times{}(5)^3+\frac{4!}{(4-4)!4!}(x)^{4-4}\times{}(5)^4

=\frac{24}{(24)1}(x)^{4-0}\times{}(5)^0+\frac{24}{(6)1}(x)^{4-1}\times{}(5)^1+\frac{24}{(2)2}(x)^{4-2}\times{}(5)^2+\frac{24}{(1)6}(x)^{4-3}\times{}(5)^3+\frac{24}{(1)24}(x)^{4-4}\times{}(5)^4 =1(x)^{4-0}\times{}(5)^0+4(x)^{4-1}\times{}(5)^1+6(x)^{4-2}\times{}(5)^2+4(x)^{4-3}\times{}(5)^3+1(x)^{4-4}\times{}(5)^4

=(x)^{4-0}\times{}(5)^0+(4)(x)^{4-1}\times{}(5)^1+(6)(x)^{4-2}\times{}(5)^2+(4)(x)^{4-3}\times{}(5)^3+(x)^{4-4}\times{}(5)^4

=(x)^{4}\times{}(5)^0+(4)(x)^{3}\times{}(5)^1+(6)(x)^{2}\times{}(5)^2+(4)(x)^{1}\times{}(5)^3+(x)^{0}\times{}(5)^4

=(x)^{4}\times{}1+(4)(x)^{3}\times{}(5)^1+(6)(x)^{2}\times{}(5)^2+(4)(x)^{1}\times{}(5)^3+1\times{}(5)^4

= x^4\times{}(1)+(4)x^3\times{}(5)+(6)x^2\times{}(25)+(4)x\times{}(125)+1\times{}(625)

= x^4 + 20x^3 + 150x^2 + 500x + 625

### FAQs on Binomial Expansion Calculator

1. What is the binomial expansion formula?

The formula to find the expansion of a binomial is (a + b)^n = ∑nk=0 (n k) an - k bk, where (n k) = n!/[(n - k)! k!] and n! = 1 . 2 . 3 ... n.

2. Define binomial expansion theorem?

A polynomial with 2 terms is called binomial. Those two terms are separated by either plus or minus symbols. The binomial theorem is the binomial expansion of the term. It is a mathematical theorem that gives the expansion of binomial when it is raised to the positive integral power.

3. How to solve the expansion of binomials?

To solve the binomial expansion of a term, you have to substitute the values in the expansion of the binomial formula and solve to get the answer.

4. How to use the binomial expansion calculator?

Enter the binomial in the input field of the calculator and press the calculate button to avail the given term expansion in a matter of seconds.