\( - 8 a ^ { 2 } m + 6 a ^ { 2 } m : a ^ { 3 } - 5 a m + m ^ { 4 } - 40 ^ { 2 } + 4 a ^ { 2 } m - 3 a m ; 7 a ^ { 2 } m - 4 a h m - 1 a a ^ { 2 } m - 3 a ^ { 2 } m + 7 a ) ^ { 2 } + 4 a m \)

Let’s dive into this expression and simplify! When combining like terms in the expression, focus on the coefficients of each term. For instance, when adding or subtracting terms with the same variable combinations—such as all the terms containing \( a^2m \)—you simply keep the variable part the same and add/subtract the coefficients. This makes it manageable to break it down step by step. For real-world applications, such expressions may seem daunting, but they represent problems in fields like physics and engineering where variables change and interact. Engineers and physicists simplify complex expressions like this when computing forces, energies, or even in computer graphics when modeling motion and collision. Understanding how to manipulate these terms is crucial in those fields!