Factoring Formulas

Posted In: Mathematics

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

Post Tags: Algebra


No Comments »


Leave a Reply

Your email address will not be published. Required fields are marked *