Important Problems on Numbers Formulas

Some Basic Formulas

  • (a + b)(a - b) = (a2 - b2)
  • (a + b)2 = (a2 + b2 + 2ab)
  • (a2 - b2) = (a2 + b2 - 2ab)
  • (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ac)
  • 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.