(3x²-y)(2x-5y²)

To simplify the expression \((3x^2 - y)(2x - 5y^2)\), you can use the distributive property (also known as the FOIL method for binomials). This involves multiplying each term in the first parentheses by each term in the second parentheses. 1. Multiply \(3x^2\) by \(2x\): \[ 3x^2 \cdot 2x = 6x^3 \] 2. Multiply \(3x^2\) by \(-5y^2\): \[ 3x^2 \cdot (-5y^2) = -15x^2y^2 \] 3. Multiply \(-y\) by \(2x\): \[ -y \cdot 2x = -2xy \] 4. Multiply \(-y\) by \(-5y^2\): \[ -y \cdot (-5y^2) = 5y^3 \] Now, combine all these products: \[ 6x^3 - 15x^2y^2 - 2xy + 5y^3 \] Thus, the expanded form of \((3x^2 - y)(2x - 5y^2)\) is: \[ 6x^3 - 15x^2y^2 - 2xy + 5y^3 \]