Multiply. \[ (5 x-2 z)(7 x+z) \] Simplify your answer.

To multiply the expressions \( (5x - 2z)(7x + z) \), we'll use the distributive property (also known as the FOIL method for binomials). 1. First, multiply \( 5x \) by \( 7x \): \[ 5x \cdot 7x = 35x^2 \] 2. Next, multiply \( 5x \) by \( z \): \[ 5x \cdot z = 5xz \] 3. Then, multiply \( -2z \) by \( 7x \): \[ -2z \cdot 7x = -14xz \] 4. Finally, multiply \( -2z \) by \( z \): \[ -2z \cdot z = -2z^2 \] Now, combine all these results: \[ 35x^2 + 5xz - 14xz - 2z^2 \] Combine the like terms \( 5xz - 14xz \): \[ 35x^2 - 9xz - 2z^2 \] So, the simplified answer is: \[ \boxed{35x^2 - 9xz - 2z^2} \]