(x²-y²)(x²+xy+y³) over (x³-y³)(x+y)​

Answer:Here's how to simplify the expression:**1. Factor the expressions:*** **Numerator:** * The first factor is a difference of squares: (x² - y²) = (x + y)(x - y) * The second factor is a sum of cubes: (x² + xy + y³) is already factored.* **Denominator:** * The first factor is a difference of cubes: (x³ - y³) = (x - y)(x² + xy + y²) * The second factor is a sum of two terms: (x + y)**2. Rewrite the expression with the factored terms:**[(x + y)(x - y)(x² + xy + y³)] / [(x - y)(x² + xy + y²)(x + y)]**3. Cancel common factors:**Notice that (x + y), (x - y), and (x² + xy + y²) appear in both the numerator and denominator. Canceling these, we are left with:**1 / 1 = 1****Therefore, the simplified expression is 1.**

Answered by danielalay732 | 2024-09-09