Newton's Binomial Calculator

Expand expressions of the form (x + y)^n

Enter a non-negative integer (maximum 50)

Result

Expression: =
Expansion: =
Value: =

About Newton's Binomial Theorem

Newton's Binomial Theorem provides a way to expand expressions of the form (x + y)^n, where n is a non-negative integer. The expansion is given by:

\[(x + y)^n = \sum_{k=0}^n \binom{n}{k} x^{n-k} y^k\]

Where:

Examples:

1. For (x + y)^2:

\[(x + y)^2 = x^2 + 2xy + y^2\]

2. For (x + y)^3:

\[(x + y)^3 = x^3 + 3x^2y + 3xy^2 + y^3\]

Applications:

Newton's Binomial Theorem has numerous applications in: