(x-y)(x²-xy-y²)

To expand the expression \((x-y)(x^2 - xy - y^2)\), we can use the distributive property (also known as the FOIL method for binomials). Here's the step-by-step expansion: 1. Distribute \(x\) to each term inside the parentheses: \[ x(x^2) - x(xy) - x(y^2) = x^3 - xyx - xy^2 \] 2. Distribute \(-y\) to each term inside the parentheses: \[ -y(x^2) + y(xy) + y(y^2) = -yx^2 + y^2x + y^3 \] Now, combine all the terms: \[ x^3 - xyx - yx^2 + y^2x + y^3 \] Next, let's simplify and rearrange the expression: \[ x^3 - x^2y + y^2x - yx^2 + y^3 \] Now, we can combine like terms: \[ x^3 - (xyx + yx^2) + (y^2x + y^3) \] Thus, the final simplified expression is: \[ x^3 - xyx - yx^2 + y^2x + y^3 \] If you would like to factor or simplify further, or if you have a different question about this expression, feel free to let me know!