# 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
$a^n-b^n=(a-b)(a^{n-1}+a^{n-2}b+a^{n-3}b^2+...+ab^{n-2}+b^{n-1})$, $a^n+b^n=(a+b)(a^{n-1}-a^{n-2}b+a^{n-3}b^2-...+ab^{n-2}-b^{n-1})$