Multiply the following and collect like terms. \[ (2 x-6) \cdot(x+5 y-8) \] Provide your answer below:

To multiply \( (2x - 6)(x + 5y - 8) \), we can use the distributive property (also known as the FOIL method for binomials). Let's distribute each term in the first parentheses to each term in the second: 1. \( 2x \cdot x = 2x^2 \) 2. \( 2x \cdot 5y = 10xy \) 3. \( 2x \cdot -8 = -16x \) 4. \( -6 \cdot x = -6x \) 5. \( -6 \cdot 5y = -30y \) 6. \( -6 \cdot -8 = 48 \) Now, let's combine all the terms: \[ 2x^2 + 10xy - 16x - 6x - 30y + 48 \] Combining like terms: - The \( x \) terms: \( -16x - 6x = -22x \) Putting it all together, we have: \[ 2x^2 + 10xy - 22x - 30y + 48 \] Thus, the final answer is: \[ 2x^2 + 10xy - 22x - 30y + 48 \]