(3х - у) * (у + 3х)

To simplify the expression \((3x - y) * (y + 3x)\), we can use the distributive property (also known as the FOIL method for binomials). Here's a step-by-step breakdown of the multiplication: 1. **First terms:** \(3x * y = 3xy\) 2. **Outer terms:** \(3x * 3x = 9x^2\) 3. **Inner terms:** \(-y * y = -y^2\) 4. **Last terms:** \(-y * 3x = -3xy\) Now, combine all these results: \[ 3xy + 9x^2 - y^2 - 3xy \] Now, combine like terms: - The \(3xy\) and \(-3xy\) cancel out. So we are left with: \[ 9x^2 - y^2 \] Thus, the simplified form of the expression \((3x - y) * (y + 3x)\) is: \[ 9x^2 - y^2 \]