Algebra - Product formulas

Real number : a,b,c
Whole numbers : n,k

  1. \((a-b)^2=a^2+2ab+b^2\)
  2. \((a+b)^2=a^2+2ab+b^2\)
  3. \((a-b)^3=a^3-3a^2b+3ab^2-b^3\)
  4. \((a+b)^3=a^3+3a^2b+3ab^2+b^3\)
  5. \((a-b)^4=a^4-4a^3b+6a^2b^2-4ab^3+b^4\)
  6. \((a+b)^4=a^4+4a^3b+6a^2b^2+4ab^3+b^4\)
  7. Binomial Formula
    \((a+b)^2={^nC_0a^n}+{^nC_1a^{n-1}b}+{^nC_2a^{n-2}b^2}+...+{^nC_{n-1}ab^{n-1}}+{^nC_nb^n},\)
    Where \(^nc_k={n! \over k!(n-k)!}\) are the binomial coefficients.
  8. \((a+b+c)^2=a^2+b^2+c^2+2ab+2ac+2bc\)
  9. \((a+b+c+...+u+v)^2=a^2+b^2+c^3+...+u^2+v^2+2(ab+ac+...+au+av+ab+...+bu+bv+...+uv)\)