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Number System and Ratio & Proportion

Some Basic Formulae

  • (a2  - b2) = (a + b)(a - b)
  • (a + b)2 = (a2 + b2 + 2ab)
  • (a - b)2 = (a2 + b2 - 2ab)
  • (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
  • (a3 + b3) = (a + b) ( a2 - ab + b2)
  • (a3 - b3) = (a - b)( a2 + ab + b2)
  • (a3 + b3 + c3 - 3abc) = (a + b + c)( a2 + b2 + c2 - ab - bc - ca)
  • When a + b + c = 0, then a3 + b3 + c3 = 3abc.
  • Sum of 1st  n odd number is
  • Sum of 1st  n even number is n*(n+1)
  • Sum of 1st  n number is
  • Sum of square of 1st n number 
  • Sum of cube of 1st n number




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