Algebra - Factoring formulas

Real numbers : a,b,c
Natural number : n

  1. \(a^2-b^2=(a+b)(a-b)\)
  2. \(a^3-b^3=(a-b)(a^2+ab+b^2)\)
  3. \(a^3-b^3=(a-b)(a^2+ab+b^2)\)
  4. \(a^3+b^3=(a+b)(a^2-ab+b^2)\)
  5. \(a^4-b^4=(a^2-b^2)(a^2+b^2)=(a-b)(a+b)(a^2+b^2)\)
  6. \(a^5-b^5=(a-b)(a^4+a^3b+a^2b^2+ab^3+b^4)\)
  7. \(a^5+b^5=(a+b)(a^4-a^3b+a^2b^2-ab^3+b^4)\)
  8. If n is odd , then
    \(a^n+b^n=(a+b)(a^{n-1}-a^{n-2}b+a^{n-3}b^2-...-ab^{n-2}+b^{n-1})\)
  9. If n is even, then
    \(a^n-b^n=(a-b)(a^{n-1}+a^{n-2}b+a^{n-3}b^2+...+ab^{n-2}+b^{n-1})\), \(a^n+b^n=(a+b)(a^{n-1}-a^{n-2}b+a^{n-3}b^2-...+ab^{n-2}-b^{n-1})\)