Mathematics

Algebra
  • $a^2 – b^2 = (a – b)(a + b)$
  • $(a+b)^2 = a^2 + 2ab + b^2$
  • $a^2 + b^2 =(a+b)^2 - 2ab$
  • $(a-b)^2 = a^2 - 2ab + b^2$
  • $(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca$
  • $(a – b – c)^2 = a^2 + b^2 + c^2 – 2ab + 2bc – 2ca$
  • $(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$
  • $(a + b)^3 = a^3 + b^3 + 3ab(a + b)$
  • $(a – b)^3 = a^3 – 3a^2b + 3ab^2 – b^3$
  • $(a – b)^3 = a^3 – b^3 – 3ab(a – b)$
  • $a^3 – b^3 = (a – b)(a^2 + ab + b^2)$
  • $a^3 + b^3 = (a + b)(a^2 – ab + b^2)$
  • $(a + b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4$
  • $(a – b)^4 = a^4 – 4a^3b + 6a^2b^2 – 4ab^3 + b^4$
  • $a^4 – b^4 = (a – b)(a + b)(a^2 + b^2)$
  • $(a^m)(a^n) = a^{m+n}$
  • $(ab)^m = a^mb^m$
  • $(a^m)^n = a^{mn}$
  • $a^0 = 1 $
  • $a^m/a^n=a^{m-n}$
  • $a^m=1/a^{-m}$
  • $a^{-m}=1/a^m$