Separate Each Term:
We will divide each term in the numerator by \( 3y^2 \):
\[
= \frac{18y^5}{3y^2} + \frac{12y^4}{3y^2} + \frac{21y^3}{3y^2} - \frac{24y^2}{3y^2}
\]
Divide Each Term:
\( \frac{18y^5}{3y^2} = 6y^{5-2} = 6y^3 \)
\( \frac{12y^4}{3y^2} = 4y^{4-2} = 4y^2 \)
\( \frac{21y^3}{3y^2} = 7y^{3-2} = 7y \)
\( \frac{24y^2}{3y^2} = 8 \)
Combine the Results:
Now we combine the results from each division:
\[
6y^3 + 4y^2 + 7y - 8
\]
Final Simplified Expression:
The final result is:
\[
6y^3 + 4y^2 + 7y - 8
\]
So, the simplified expression for \( \frac{18y^5 + 12y^4 + 21y^3 - 24y^2}{3y^2} \) is \( 6y^3 + 4y^2 + 7y - 8 \).