4. \( 2 m^{2}+15+2 p^{2} \)

Let’s delve into a little mathematical fun! The expression \( 2m^2 + 15 + 2p^2 \) is a combination of like terms and constants; it showcases quadratic terms \( m^2 \) and \( p^2 \) multiplied by 2, alongside a constant 15. Quadratics are pivotal in various mathematical disciplines, including algebra and calculus, as they often represent trajectories in physics and optimization problems in economics! Now, if you're looking to make this expression factorable, you could explore completing the square or finding roots if set equal to zero. Common mistakes include overlooking the conditions under which a quadratic can be factored or neglecting to check for completeness in terms. Don't forget to double-check your calculations—sometimes a tiny slip can lead to a whole new direction in problem-solving!