Find the product and simplify. \( (3 y+5)(-3 y+5) \)

To find the product of \( (3y + 5)(-3y + 5) \), we can use the distributive property, also known as the FOIL method for binomials. First, we multiply the first terms: \( 3y \cdot (-3y) = -9y^2 \). Next, we multiply the outer terms: \( 3y \cdot 5 = 15y \). Then, we multiply the inner terms: \( 5 \cdot (-3y) = -15y \). Finally, we multiply the last terms: \( 5 \cdot 5 = 25 \). Now, we combine all those results: \[ -9y^2 + 15y - 15y + 25 \] The \( 15y \) and \( -15y \) cancel each other out, leaving us with: \[ -9y^2 + 25. \] Thus, the simplified product is \( -9y^2 + 25 \).