Square of Difference Calculator (a-b)²
Calculate the square of a difference for algebraic terms. Visualizes the substitution into the formula a² - 2ab + b² to prevent common sign errors.
About
Expanding the square of a difference is a fundamental skill in algebra, governed by the formula (a − b)2 = a2 − 2ab + b2. Errors frequently occur in the middle term (forgetting the factor of 2) or the sign of the final term (which must always be positive). This tool allows users to input complex terms involving coefficients and exponents. It performs the symbolic substitution and simplification, ensuring that terms like (3x)2 are correctly expanded to 9x2 rather than 3x2.
Formulas
The calculator breaks down the expression into three distinct components:
If terms contain coefficients c and variables v, the squaring operation follows (cv)2 = c2v2.
Reference Data
| Term A | Term B | Expansion (a − b)2 |
|---|---|---|
| x | 1 | x2 − 2x + 1 |
| 2x | 3 | 4x2 − 12x + 9 |
| x2 | y | x4 − 2x2y + y2 |
| 5a | 2b | 25a2 − 20ab + 4b2 |
| 1 | x | 1 − 2x + x2 |
| x | 0.5 | x2 − x + 0.25 |
| 3m | 4n2 | 9m2 − 24mn2 + 16n4 |
| 10 | z | 100 − 20z + z2 |