Cube of Sum Calculator
Calculate (a + b)³ expansions accurately. Handles complex coefficient multiplication and powers for cubic binomials, perfect for advanced algebra verification.
About
Expanding a binomial to the third power requires precision that mental math often lacks. The complexity jumps significantly from a square to a cube, as intermediate terms involve squaring one coefficient while multiplying by another. This tool automates the Binomial Theorem for degree 3, ensuring that the coefficients 1, 3, 3, 1 are applied correctly to the powers of your specific variables. It is essential for students dealing with higher-order polynomials where a single arithmetic slip renders the final function incorrect.
Formulas
The expansion follows the Binomial Theorem for n=3. The general form consists of four terms with specific combinatorial weights.
If a has a coefficient A and b has a coefficient B, the second term becomes:
Reference Data
| N | Polynomial | Expansion (Pascal's Triangle) |
|---|---|---|
| 0 | (a + b)0 | 1 |
| 1 | (a + b)1 | 1a + 1b |
| 2 | (a + b)2 | 1a2 + 2ab + 1b2 |
| 3 | (a + b)3 | a3 + 3a2b + 3ab2 + b3 |
| 4 | (a + b)4 | a4 + 4a3b + 6a2b2 + ... |
| Example | (2x + 1)3 | 8x3 + 12x2 + 6x + 1 |
| Example | (x - 2)3 | x3 − 6x2 + 12x − 8 |
| Logic | Coefficients | Sum of the two numbers directly above in Pascal's Triangle |