1) \( \left(5 p^{2}-3\right)+\left(2 p^{2}-3 p^{3}\right) \)

First, let's combine like terms. Start by grouping all the \( p^2 \) and \( p^3 \) terms together: \[ (5p^2 + 2p^2 - 3p^3 - 3) = (7p^2 - 3p^3 - 3). \] So, the simplified expression is: \[ -3p^3 + 7p^2 - 3. \] Now, you can see how combining algebraic expressions works by pooling similar factors together, which is an essential skill in both academic math and practical applications like budgeting or planning! If you want to explore polynomial expressions further, consider looking into factoring techniques or the role of polynomials in defining curves in calculus – it’s a foundational concept that leads into more advanced math topics and real-world applications in engineering and physics!