Algebra Factoring Formulas
Real numbers: a, b, c
Natural number: n
1. a2 –b2 = (a+b)(a-b)
2. a3 –b3 = (a-b)( a2 +ab +b2)
3. a3 +b3 = (a+b)( a2 -ab +b2)
4. a4 –b4 = (a2-b2)(a2 + b2) = (a – b)(a + b)(a2 +b2)
5. a5 – b5 = (a –b ) (a4 +a3b +a2b2 +ab3 +b4)
6. a5 + b5 = (a +b ) (a4 -a3b +a2b2 -ab3 +b4)
7. If n is odd, than
an + bn = (a +b) (an-1 – an-2b + an-3b2– ….-abn-2 +bn-1).
8. If n is even, taan
an – bn = (a -b) (an-1 + an-2b + an-3b2+ ….+abn-2 +bn-1).