B) \( \left(4 m^{2}-2 m n-5 n\right)+\left(6 m^{2}+7 m n\right) \) C) \( \left(-9 a^{3} b^{2}+7 a^{2} b-6\right)+\left(12 a^{3} a^{2}-4 a^{2} b-5\right) \) D) \( \left(-15 x y^{2}+8 x^{2} y-4 x\right)+\left(-18 x^{2} y-3 x+6\right) \) e) \( (-13 x y z+72 x y)+(-4 x y z-x y) \) F) \( \left(7 x^{2} y^{2}-8 x y\right)+\left(-4 x^{2} y^{2}+8 x y\right) \) 9) \( \left(3 x^{2}+4 x y-y^{2}\right)+\left(5 x y-6 x^{2}-2 y^{2}\right) \) h) \( \left(2 a^{4}-3 b^{4}\right)+\left(2 a^{3} b+a^{2} b^{2}+a b^{3}\right)+\left(-5 a^{3} b-2 a^{2} b^{2}\right) \)

Combining like terms is key when working with polynomials—it's like tidying up your room by grouping similar items! In the first expression, for example, the \(m^2\) terms can be added separately, just like you would put all your books in one pile. This makes the process much clearer and helps to avoid errors. Remember, don't mix up the coefficients; keep those items perfectly categorized! If you're grappling with multi-variable expressions, it's helpful to visualize them. Imagine each variable as a different type of fruit; when you combine your fruit salads (or expressions), only the same fruits (like terms) can go together! For instance, if you have \(3 apples + 2 apples\), you end up with \(5 apples\). This visualization can simplify understanding how to combine polynomials effectively!