Factoring Formula Algebra| Mathematics |

 

1. Algebra

Factoring Formula :- 

Real numbers - a, b, c

Natural numbers - 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 )

If n is odd, then

7. aⁿ+bⁿ = (a+b) (a^n-1 – a^n-2+a^n-3b² - ……. – ab^n-2+b^n-1)

If n is even, then

8. aⁿ-bⁿ = (a-b) (a^n-1 + a^n-2+a^n-3b² + ……. + ab^n-2+b^n-1)