In order to sum the given expressions, simplify like terms (terms with same variable of the same order), then, you have:
(4z^3+8z^2−z) + (−4z^2+z+7)
= 4z^3 + 8z^2 −z −4z2 + z + 7
= 4z^3 + 4z^2 + 7
Hence, the result of the sum of the given expressions is
4z^3 + 4z^2 + 7
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