Algebra

Algebra

Points to remember:
 
1. The sum of the first n odd numbers               =   n^2

2. The sum of the first n even numbers             =   n(n+1)

3. The sum of the first n consecutive numbers  =   n(n+1) divided by 2

4. Sum of numbers 51 to 100  = ?
    [Hint here 51 = a, 100 = last number;
       Sum = number of terms divided by 2
                   multiplied by (a + last number)
      Hence sum = 50 divided by 2
                            mutliplied by (51 + 100)
                        = 25 x 151  =  3775]

5. The number of  hand-shake of n persons       =   n(n-1) divided by 2

6. n^th odd number                                            =   2n-1
    [e.g.100 th odd number is 2(100-1) = 199]

7. n^th term                                                        =   a + (n - 1) d

8. Distributive property :  a(b+c) = ab + ac

9. Cross-Product Rule:
     If a divided by b = c divided by d is true, a x d = b x c is also true.

10. Product of extremes = Product of means.

11. Product of any number  and zero = Zero

12. (Any number)^0                         = 1.

13. (a + b)^2    =  a^2 + b^2 + 2ab

14. (a - b)^2     =  a^2 + b^2 - 2ab

15. a^2 - b^2    =  (a + b) (a - b)

16. (a + b)^2 - (a - b)^2 divided by ab  = 4ab divided by ab = 4

17. a^3 + b^3 divided by a^2 - ab + b^2  = a + b

18. a^m  x   a^ n                =  a^(m+n)

19. a^m  divided by  a^n   =  a^(m-n)      

20. 2^10  = 1024