Binomial Expansion Calculator

This tool applies the binomial theorem to an expression of the form (a x + b) raised to a whole number power. Give a, b and the power, and it returns the full expansion in descending powers along with the row of Pascal's triangle it came from and the arithmetic behind every coefficient. A second tab returns a single term on its own, which is what most homework questions actually ask for. It works on numbers you type into boxes rather than on typed algebra, so a trinomial or a fractional power is outside what it can do.

Calculator Type

Every term of (a x + b)^n, in descending powers.

The a in (a x + b)^n. Put 1 in for a plain x.
Negative for a subtraction, so (x - 2)^5 has b = -2.
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The r-th term of the expansion, counting from the highest power.

The a in (a x + b)^n. Put 1 in for a plain x.
Negative for a subtraction, so (x - 2)^5 has b = -2.
The first term is the one with the highest power of the variable.
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