(x-y)(x²-xy-y²)

You have the expression \((x - y)(x^2 - xy - y^2)\). To simplify or expand it, we can use the distributive property (also known as the FOIL method for binomials). Let's expand the expression step by step: \[ (x - y)(x^2 - xy - y^2) = x(x^2 - xy - y^2) - y(x^2 - xy - y^2) \] Now we will distribute both terms: 1. **For \(x(x^2 - xy - y^2)\)**: \[ x \cdot x^2 - x \cdot xy - x \cdot y^2 = x^3 - xyx - xy^2 = x^3 - x^2y - xy^2 \] 2. **For \(-y(x^2 - xy - y^2)\)**: \[ -y \cdot x^2 + y \cdot xy + y \cdot y^2 = -yx^2 + y^2x + y^3 = -x^2y + y^2x + y^3 \] Now combine everything together: \[ = x^3 - x^2y - xy^2 - x^2y + y^2x + y^3 \] Combining like terms: \[ = x^3 - 2x^2y + y^2x - xy^2 + y^3 \] Thus, the expanded form of the expression \((x - y)(x^2 - xy - y^2)\) is: \[ = x^3 - 2x^2y + y^2x - xy^2 + y^3 \]