ploynomials

Question

(x^3+y^3)/(x-y) how do i figure this out?

Answer 1

The sum of cubes states that a³ + b³ = (a + b)(a² - ab + b²)

Using the sum of cubes, we can factor the numerator:

[(x + y)(x² - xy + y²)]/(x - y)

Since there are no common factors of then numerator and denominator, the fraction cannot be reduced.

 

Note that if the numerator were x³ - y³, the factors would be (x - y)(x² + xy +y²), which could be reduced.