Math Formulae: Algebraic Identities

Here are some important algebraic Identities: 

1. (a + b)² = a² + 2ab + b²
   
   
2. (a - b)² = a² - 2ab + b²
   
   
3. (a + b)³ = a³ + b³ + 3ab(a + b)
          = a³ +3a²b + 3ab² + b³
   
   
4. (a - b)³ = a³ - b³ - 3ab(a - b)
          = a³ - 3a²b + 3ab² - b³
   
   
5. a² - b² = (a - b).(a + b)
   
   
6. (a + b)² + (a - b)² = 2a² + 2b²
   
   
7. (a + b)² - (a - b)² = 4ab
   
   
8. a³ + b³ = (a + b).(a² - ab + b²)
   
   
9. a³ - b³ = (a - b).(a² + ab + b²)
   
   
10. a³ + b³ + c³ - 3abc = (a + b + c).(a² + b² + c² - ab - bc - ca)
    if a + b + c = 0,
    then a³ + b³ + c³ = 3abc
    
    
11. (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
    
    
12. 1 + 2 + 3 + ....... + n = 

    	n(n+1)
    	2

    
    
    
13. 1² + 2² + 3² + ....... + n² = 

    	n(n+1)(2n+1)
    	6

    
    
    
14. 1³ + 2³ + 3³ + ....... + n³ = 

    	(	n(n+1)	)2
    		2

    
    
    
15. sum of 1st n odd numbers = n²
    
    
16. sum of 1st n even numbers = n(n+1)
    
    
17. if aⁿ = a^m, then n = m
    
    
18. if aⁿ = bⁿ,
    then a = b, (if n is odd), and
    a = +b or -b (if n is even)
    

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