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Algebraic identities formulas
17 formulas for Algebraic identities, from the Algebra section of the Quantix formula library. Tap 🧮 next to a formula to solve it for any variable with step-by-step working.
| Name | Formula | Note |
|---|---|---|
| Square of a sum | (a + b)² = a² + 2ab + b² | |
| Square of a difference | (a − b)² = a² − 2ab + b² | |
| Difference of squares | a² − b² = (a + b)(a − b) | |
| Cube of a sum | (a + b)³ = a³ + b³ + 3ab(a + b) | |
| Cube of a difference | (a − b)³ = a³ − b³ − 3ab(a − b) | |
| Sum of cubes | a³ + b³ = (a + b)(a² − ab + b²) | |
| Difference of cubes | a³ − b³ = (a − b)(a² + ab + b²) | |
| Square of a trinomial | (a + b + c)² = a² + b² + c² + 2(ab + bc + ca) | |
| Three cubes | a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca) | |
| Three cubes — special case | If a + b + c = 0, then a³ + b³ + c³ = 3abc | |
| Sum of squares | a² + b² = (a + b)² − 2ab = (a − b)² + 2ab | |
| (a + b)² − (a − b)² | = 4ab | |
| (a + b)² + (a − b)² | = 2(a² + b²) | |
| Fourth powers | a⁴ − b⁴ = (a − b)(a + b)(a² + b²) | |
| Product of binomials | (x + a)(x + b) = x² + (a + b)x + ab | |
| Sophie Germain | a⁴ + 4b⁴ = (a² + 2b² + 2ab)(a² + 2b² − 2ab) | |
| aⁿ − bⁿ | (a − b)(aⁿ⁻¹ + aⁿ⁻²b + … + bⁿ⁻¹) |
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