**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^{4} –b^{4} = (a^{2}-b^{2})(a^{2} + b^{2}) = (a – b)(a + b)(a^{2} +b^{2})

5. a^{5} – b^{5} = (a –b ) (a^{4} +a^{3}b +a^{2}b^{2} +ab^{3} +b^{4})

6. a^{5} + b^{5} = (a +b ) (a^{4} -a^{3}b +a^{2}b^{2} -ab^{3} +b^{4})

7. If n is odd, than

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, taan

a^{n} – b^{n} = (a -b) (a^{n-1 }+ a^{n-2}b + a^{n-3}b^{2}+ ….+ab^{n-2 }+b^{n-1}).