Distributive Property Calculator (Expanding Brackets)
Expand algebraic expressions using the distributive property and FOIL method. Visualizes term multiplication for binomials and complex nested brackets.
About
Factorizing is useful for finding roots, but expansion is essential for simplification and solving linear differential equations. This tool focuses on the "Expansion" phase of algebra, specifically applying the Distributive Law to remove parentheses. It is particularly useful when checking manual work on complex nested expressions where keeping track of negative signs is difficult.
The calculator employs the FOIL method (First, Outer, Inner, Last) logic for binomials but generalizes this to any polynomial multiplication. It breaks down the process term-by-term, ensuring that every element in the first polynomial multiplies every element in the second. This prevents the common "Freshman's Dream" error where students incorrectly assume x+y2 equals x2+y2.
Formulas
The General Distributive Law for any number of terms is:
When expanding (x + a)n, the coefficients are determined by the combination formula:
Reference Data
| Identity Name | Formula | Use Case |
|---|---|---|
| Square of Sum | (a+b)2 = a2 + 2ab + b2 | Parabolic expansion |
| Square of Diff | (a−b)2 = a2 − 2ab + b2 | Parabolic expansion |
| Diff of Squares | (a+b)(a−b) = a2 − b2 | Rationalizing denominators |
| Cube of Sum | (a+b)3 = a3 + 3a2b + 3ab2 + b3 | Volume expansion |
| Sum of Cubes | a3+b3 = (a+b)(a2−ab+b2) | Factoring cubic roots |
| FOIL Rule | (a+b)(c+d) = ac + ad + bc + bd | General binomials |
| Pascal Row 4 | 1, 4, 6, 4, 1 | Coefficients for power 4 |
| Pascal Row 5 | 1, 5, 10, 10, 5, 1 | Coefficients for power 5 |