Square Formulas

• 1. (a + b)² = a² + 2ab + b²
• 2. (a − b)² = a² − 2ab + b²
• 3. a² + b² = (a + b)² − 2ab
• 4. a² + b² = (a − b)² + 2ab
• 5. a² + b² = ½{(a + b)² + (a – b)²}
• 6. a² − b² = (a + b)(a − b)

Cube Formulas

• 1. (a + b)³ = a³ + b³ + 3ab(a + b)
• 2. (a − b)³ = a³ − b³ − 3ab(a − b)
• 3. a³ + b³ = (a + b)³ − 3ab(a + b)
• 4. a³ − b³ = (a − b)³ + 3ab(a − b)
• 5. a³ − b³ = (a − b)(a² + ab + b²)
• 6. a³ + b³= (a + b)(a² − ab + b²)

All other Algebra Formulas

• a⁴ – b⁴ = (a² – b²)(a² + b²) = (a + b)(a – b)(a² + b²)
• a⁴ + b⁴ = (a² + b²)² – 2a²b² = (a² + √2ab + b²)(a² – √2ab + b²)
• a⁵ + b⁵ = (a + b)(a⁴ – a³b + a²b² – ab³ + b⁴ )
• a⁵ – b⁵ = (a – b)(a⁴ + a³b + a²b² + ab³ + b⁴)
• aⁿ − bⁿ = (a − b)(aⁿ⁻¹ + aⁿ⁻² b + aⁿ⁻³ b² + ··· + bⁿ⁻¹n−1)
• (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
• a³ + b³ + c³ – 3abc = (a + b + c)(a² + b² + c² – ab – bc – ca)
• If a + b + c = 0, then the above identity reduces to a³ + b³ + c³ = 3abc