(x - y)(x² + xy + y²)

1 answer

When expanding the expression, we use the distributive property:

(x - y)(x² + xy + y²) = x(x² + xy + y²) - y(x² + xy + y²)

Expanding each product individually, we get:

= x * x² + x * xy + x * y² - y * x² - y * xy - y * y²

Simplifying each term, we have:

= x³ + x²y + xy² - x²y - xy² - y³

Combining like terms, we can see that the terms x²y and -x²y, as well as xy² and -xy², cancel out:

= x³ - y³

Therefore, (x - y)(x² + xy + y²) simplifies to x³ - y³.