🧮 Binomial Expansion Calculator — (a + b)ⁿ

Expand any binomial such as (2x + 3)⁵ or (x − 1/y)⁸ term by term, with Pascal's triangle, the binomial coefficients, a “find term k” locator and Newton's generalised (1 + x)ⁿ approximation for fractional and negative powers.

Type each term as a plain monomial — coefficient, letter and power: 2x, -3y^2, x^5, 0.5t^3, or just 4 for a constant. Exponents may be negative (b = y^-1).

First term a

Second term b

Power n (0–30)

Find term number k (1 = first)

The expansion

Coefficients, row by row

Newton's approximation trick

For small x, (1 + x)ⁿ works for any real n — even negative and fractional powers — as an infinite series. Useful for mental maths and physics linearisation.

x (|x| < 1)

n (any real)

Pascal's triangle

Row n holds the coefficients of (a + b)ⁿ — highlighted above.