Polynomial Squaring & Expansion Calculator
Instantly expand binomials and polynomials like (ax + by)^2. Visualize the FOIL method and avoid common algebraic errors.
About
Algebraic expansion is a fundamental skill in mathematics, yet it remains a frequent source of errors for students and professionals alike. The most common mistake is forgetting the cross-terms when squaring a binomial. This tool automates the expansion of squared polynomials, ensuring every term is accounted for. It handles coefficients, multiple variables, and negative signs with precision. Whether you are simplifying complex algebraic structures or double-checking a calculus derivative setup, this engine breaks down the squared expression into its constituent parts instantly.
Formulas
The general expansion rule for squaring a polynomial relies on distributing every term against every other term.
Reference Data
| Expression Type | Formula Pattern | Expanded Result |
|---|---|---|
| Binomial Square (Sum) | (a + b)2 | a2 + 2ab + b2 |
| Binomial Square (Diff) | (a − b)2 | a2 − 2ab + b2 |
| Trinomial Square | (a + b + c)2 | a2 + b2 + c2 + 2(ab + bc + ca) |
| Difference of Squares | (a + b)(a − b) | a2 − b2 |
| Cube of Sum | (a + b)3 | a3 + 3a2b + 3ab2 + b3 |
| Zero Exponent | (x + y)0 | 1 |
| Identity | (x + y)1 | x + y |