Binomial Theorem Calculator

The binomial theorem calculator helps you to find the expanding binomials for the given binomial equation.

No doubt, the binomial expansion calculation is really complicated to express manually, but this handy binomial expansion calculator follows the rules of binomial theorem expansion to provide the best results.

What is Binomial Theorem?

In mathematics, a polynomial that has two terms is known as binomial expression. These two terms will always be separated by either a plus or minus and appears in term of series.

This series is known as a binomial theorem. It can also be defined as a binomial theorem formula that arranges for the expansion of a polynomial with two terms.

Binomial Theorem Formula:

A binomial expansion calculator automatically follows this systematic formula so it eliminates the need to enter and remember it. The formula is:

• If \( n ∈N,x,y,∈ R \) then

$$^nΣ_{r=0}= ^nC_r x^{n-r} y^r + ^nC_r x^{n-r}· y^r + …………. +  ^nC_{n-1}x · y^{n-1}+ ^nC_n · y^n$$

$$ e. (x + y)^n = ^nΣ_r=0 ^nC_rx^{n – r} · yr $$

where,

$$ ^nC_r = n / (n-r)^r $$

it can be written in another way:

$$(a+ b)^n = ^nC_0a^n + ^nC_1a^{n-1}b + ^nC_2a^{n-2}b^2 + ^nC_3a^{n-3}b^3 + … + ^nC_nb^n$$

How to Expand Binomials?

You can use the binomial theorem to expand the binomial. To carry out this process without any hustle there are some important points to remember:

• The number of terms in the expansion of \( (x+y)^n \) will always be \( (n+1) \)
• If we add exponents of x and y then the answer will always be n.
• Binomial coffieicnts are \( ^nC_0, ^nC_1, ^nC_2, … ..,^nC_n \). Anotherr way to represent them is: \( C_0, C_1, C_2, ….., C_n \).
• All those binomial coefficients that are equidistant from the start and from the end will be equivalent. For example: \( ^nC_0 = ^nC_n, ^nC_{1} = ^nC_{n-1} , nC_2 = ^nC_{n-2} ,….. \) etc.

How Binomial Theorem Calculator Works?

Binominal theorem calculator works steadily and quickly. Follow the simple steps explained below:

Input:

• first of all, enter a binomial term in the respective filed
• enter the power value
• hit the calculate button

Output:

• This binomial series calculator will display your input
• All the possible expanding binomials.

References:

• From the source of Boundless Algebra: Binomial Expansion and Factorial Notation.
• From the source of Magoosh Math: Binomial Theorem, and Coefficient.