Basic Algebraic Formulas

Basic Algebraic Formulas

1. (a + b)² = a² + 2ab + b²
                 = (a – b)² + 4ab
 2. (a – b)² = a² + 2ab + b²
                 = (a – b)² + 4ab
 3. (a + b)³ = a³ + 3a²b + 3ab² + b³
                  = a³ + b³ + 3ab(a + b)
 4. (a – b)³  = a³ – 3a²b + 3ab² – b³
                  = a³ – b³ – 3ab(a – b)
 5. a² + b²  = (a + b)² – 2ab
                  = (a – b)² + 2ab
                  = [ (a + b)² + (a – b)² ]
 6. a² – b²   = (a + b)(a – b)
 7. a³ + b³  = (a + b)(a² – ab + b²)
                  = (a + b)³ – 3ab(a + b)
 8. a³ – b³   = (a – b)(a² + ab + b²)
                  = (a – b)³ + 3ab(a – b)
 9. 4ab       = (a + b)² – (a – b)²
10. ab        = [(a + b)/2]² – [(a – b)/2]²

Some Special Formulas: 

1. (a + b + c)²

= a² + b² + c² + 2ab + 2bc + 2ca
2. a² + b² + c² + ab + bc + c

= [(a + b)² + (b + c)² + (c + a)²] 3. a² + b² + c² – ab – bc – ca

= [(a – b)² + (b – c)² + (c – a)²] 4. a³ + b³ + c³ – 3abc

= (a + b + c)(a² + b² + c² – ab – bc – ca)
= (a + b + c)[(a – b)² + (b – c)² + (c – a)²]