(- a ^ 3 * z ^ 2 + 5a ^ 2 * z ^ 2 - 5a ^ 2 * z ^ 3)+(- 3a ^ 2 * z ^ 2 + 7a ^ 2 * z ^ 3)

The expression you provided is a polynomial. To simplify it, we can combine like terms. Like terms are terms that have the same variables and powers.

The given expression is:

(- a ^ 3 * z ^ 2 + 5a ^ 2 * z ^ 2 - 5a ^ 2 * z ^ 3)+(- 3a ^ 2 * z ^ 2 + 7a ^ 2 * z ^ 3)

First, let's rearrange the terms so that like terms are together:

= - a ^ 3 * z ^ 2 + 5a ^ 2 * z ^ 2 - 3a ^ 2 * z ^ 2 - 5a ^ 2 * z ^ 3 + 7a ^ 2 * z ^ 3

Now, let's combine like terms:

= - a ^ 3 * z ^ 2 + (5a ^ 2 * z ^ 2 - 3a ^ 2 * z ^ 2) + (- 5a ^ 2 * z ^ 3 + 7a ^ 2 * z ^ 3)

= - a ^ 3 * z ^ 2 + 2a ^ 2 * z ^ 2 + 2a ^ 2 * z ^ 3

So, the simplified form of the given expression is - a ^ 3 * z ^ 2 + 2a ^ 2 * z ^ 2 + 2a ^ 2 * z ^ 3.