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Wednesday, 4 January 2017

29 Popular Algebraic formulas in mathematics

Following are a list of Algebraic formulas


  1. a2 – b2 = (a – b)(a + b)
  2. (a+b)2 = a2 + 2ab + b2
  3. a2 + b2 = (a – b)2 – 2ab
  4. (a – b)2 = a2 – 2ab + b2
  5. (a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc
  6. (a – b – c)2 = a2 + b2 + c2 – 2ab – 2ac + 2bc
  7. (a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
  8. (a – b)3 = a3 – 3a2b + 3ab2 – b3
  9. a3 – b3 = (a – b)(a2 + ab + b2)
  10. a3 + b3 = (a + b)(a2 – ab + b2)
  11. (a + b)3 = a3 + 3a2b + 3ab2 + b3
  12. (a – b)3 = a3 – 3a2b + 3ab2 – b3
  13. (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4)
  14. (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4)
  15. a4 – b4 = (a – b)(a + b)(a2 + b2)
  16. a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)
  17. If n is a natural number, an – bn = (a – b)(an-1 + an-2 +…+ bn-2a + bn-1)
  18. If n is even (n = 2k), an + bn = (a + b)(an-1 – an-2b +…+ bn-2a – bn-1)
  19. If n is odd (n = 2k + 1), an + bn = (a + b)(an-1 – an-2b +…- bn-2a + bn-1)
  20. (a + b + c + …)2 = a2 + b2 + c2 + … + 2(ab + ac + bc + ….
  21. Laws of Exponents
  22. (am)(an) = am+n
  23. (ab)m = ambm
  24. (am)n = amn
  25. Fractional Exponents
  26. a0 = 1
  27. aman=am−naman=am−n
  28. amam = 1a−m1a−m
  29. a−ma−m = 1am



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