Expand expressions of the form (ax + by)^n using the binomial theorem.
Input Expression
(1x + 1y)^3
Expansion Result
x^3 + 3x^2y + 3xy^2 + y^3
Expanded Form
The polynomial resulting from multiplying the binomial by itself n times.
Total Terms4
TypePolynomial
Coefficient Distribution
About this calculator
Expanding Binomials
Binomial expansion is the process of writing the product of a binomial (like x + y) raised to a power (n) as a sum of terms. Instead of multiplying term-by-term (FOIL), we use the Binomial Theorem which leverages binomial coefficients (nCr) to find the entries directly.
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Pro Tips
The powers of x decrease from n to 0 across the expansion.
The powers of y increase from 0 to n across the expansion.
The sum of exponents in each term always equals n.
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Fun Facts
"The coefficients follow the pattern of Pascal's Triangle."
"The number of terms in the expansion is always n + 1."
"Sir Isaac Newton generalized the binomial theorem for non-integer exponents, which led to the development of calculus."
