Final answer:
Dividing the polynomial (x^3 + y^3) by (x - y) results in (x^2 - xy + y^2), which is a standard result derived from algebraic identities.
Step-by-step explanation:
When dividing the polynomial (x^3 + y^3) by (x - y), we are essentially looking to factor the numerator and cancel out the denominator. This is a well-known algebraic identity where a^3 + b^3 = (a + b)(a^2 - ab + b^2). In this case, a is x and b is y, allowing us to rewrite the expression as (x + y)(x^2 - xy + y^2). When we divide by (x - y), (x + y) and (x - y) are not the same and cannot cancel each other out, but this process still helps us to recognize the correct answer. Therefore, the fraction simplifies to the polynomial (x^2 - xy + y^2).