(5x2+3)(3-5x2)

To simplify the expression \((5x^2 + 3)(3 - 5x^2)\), we can use the distributive property (also known as the FOIL method for binomials): 1. **Multiply the first terms**: \[ 5x^2 \cdot 3 = 15x^2 \] 2. **Multiply the outer terms**: \[ 5x^2 \cdot (-5x^2) = -25x^4 \] 3. **Multiply the inner terms**: \[ 3 \cdot 3 = 9 \] 4. **Multiply the last terms**: \[ 3 \cdot (-5x^2) = -15x^2 \] Now, combine all these results together: \[ 15x^2 - 25x^4 + 9 - 15x^2 \] Now combine like terms: - The \(15x^2\) and \(-15x^2\) cancel each other out. This leaves us with: \[ -25x^4 + 9 \] Thus, the simplified expression is: \[ \boxed{-25x^4 + 9} \]