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.
(x - y)(x² + xy + y²)
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