Binomial Expansion Calculator
Our Binomial Expansion Calculator helps you quickly expand expressions in the form of (a + b)^n. Whether you're tackling algebra homework or exploring advanced polynomial concepts, this tool simplifies the process of finding each term and coefficient.
Enter the numerical coefficient for 'a' (e.g., 2 for 2x).
Enter the numerical coefficient for 'b' (e.g., 3 for +3).
Enter the non-negative integer power.
Our Binomial Expansion Calculator helps you quickly expand expressions in the form of (a + b)^n. Whether you're tackling algebra homework or exploring advanced polynomial concepts, this tool simplifies the process of finding each term and coefficient.
(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^kLet's expand (2x + 3)^3. Here, 'a' is the coefficient 2 (for 2x), 'b' is the constant 3, and 'n' is the power 3. Using the binomial theorem, we find the coefficients and terms: (2x + 3)^3 = \binom{3}{0}(2x)^3(3)^0 + \binom{3}{1}(2x)^2(3)^1 + \binom{3}{2}(2x)^1(3)^2 + \binom{3}{3}(2x)^0(3)^3 = 1(8x^3)(1) + 3(4x^2)(3) + 3(2x)(9) + 1(1)(27) = 8x^3 + 36x^2 + 54x + 27 Simply input '2' for 'Coefficient a', '3' for 'Coefficient b', and '3' for 'Power n' into the calculator to see this result.
Binomial expansion is a method for expanding algebraic expressions that are powers of binomials (expressions with two terms), such as (x + y)^n. The Binomial Theorem provides a formula to find each term in the expanded form without direct multiplication.
The Binomial Theorem uses binomial coefficients, often found in Pascal's Triangle, to determine the numerical part of each term. For an expression (a + b)^n, the terms follow a pattern where the power of 'a' decreases from 'n' to 0, and the power of 'b' increases from 0 to 'n'.
Our calculator is designed for non-negative integer powers ('n'). While the binomial theorem can be extended to negative or fractional powers using infinite series, this tool focuses on the standard finite expansion taught in school algebra.
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