short answer. find the following product -7z(-8z^3+3z^2+8)

Go ahead and multiply term by term.

To find the product of -7z and (-8z^3 + 3z^2 + 8), we need to distribute -7z to each term inside the parentheses.

We multiply -7z by -8z^3:
-7z * -8z^3 = 56z^4

Next, we multiply -7z by 3z^2:
-7z * 3z^2 = -21z^3

Lastly, we multiply -7z by 8:
-7z * 8 = -56z

Putting it all together, the product of -7z and (-8z^3 + 3z^2 + 8) is:
56z^4 - 21z^3 - 56z