Binomial Expansion Calculator

Enter values for X, Y, and n to for expansion of binomial term using binomial expansion calculator.

Equation: (X + Y) n

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Binomial expansion calculator expands the binomial expression using binomial theorem. Enter required values and click the Calculate button to get the result with expansion using binomial theorem calculator.

Binomial theorem - Definition/Formula

For any positive integer n, the nth power of the sum of two numbers a and b may be expressed as the sum of n + 1 terms of the form.

The equation of binomial theorem is,

Binomial expansion


n ≥ 0 is an integer,

(n, k) is binomial coefficient.

The fully expanded form of higher exponents can also be calculated using the binomial expansion formula.

Binomial formula

Examples of Binomial theorem:


What is the expanded form of binomial expression (3 + 5)^4?


Step 1:  Expand the expression:      
   binomial example

Step 2: Find the values of binomial coefficients:
binomial example

Step 3:  put the values of coefficients and solve:

Binomial example

The binomial theorem calculator gives the solution with steps. 

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