Let's simplify each of the given expressions step by step.
First Expression:
\[ \frac{21s^3 - 3s^2}{-3} \]
We can factor out \(-3\) from the denominator and split the fraction: \[ = -\frac{21s^3 - 3s^2}{3} \]
Now, simplify the numerator: \[ = -\left(\frac{21s^3}{3} - \frac{3s^2}{3}\right) \] \[ = -\left(7s^3 - s^2\right) \] \[ = -7s^3 + s^2 \] or \[ s^2 - 7s^3 \]
Second Expression:
\[ \frac{-18z^5 + 3z^4 + 18z^3 + 9z^2}{-3z^2} \]
We can split the fraction: \[ = \frac{-18z^5}{-3z^2} + \frac{3z^4}{-3z^2} + \frac{18z^3}{-3z^2} + \frac{9z^2}{-3z^2} \]
Each term simplifies as follows:
- \(\frac{-18z^5}{-3z^2} = 6z^{3}\)
- \(\frac{3z^4}{-3z^2} = -z^{2}\)
- \(\frac{18z^3}{-3z^2} = -6z^{1}\)
- \(\frac{9z^2}{-3z^2} = -3\)
Combining these gives: \[ = 6z^3 - z^2 - 6z - 3 \]
Third Expression:
\[ -(-6z^3) - z^2 - 6z - 3 \]
When we simplify: \[ = 6z^3 - z^2 - 6z - 3 \]
Final Overview
Both expressions, when simplified, yield the same result:
The first expression simplified gives: \[ s^2 - 7s^3 \]
The second expression simplified gives: \[ 6z^3 - z^2 - 6z - 3 \]
The final expression too simplifies to: \[ 6z^3 - z^2 - 6z - 3 \]
So the simplified results are:
- \(s^2 - 7s^3\)
- \(6z^3 - z^2 - 6z - 3\)
Let me know if you need further assistance with any of these expressions!