To subtract the given polynomials, we follow these steps:
1. Write down the polynomials in their original form:
[tex]\[
\left(-8 y^2 - 9 y\right) - \left(-8 y^3 + 9 y^2 - 5 y\right)
\][/tex]
2. Distribute the negative sign to the second polynomial:
[tex]\[
-8 y^2 - 9 y - (-8 y^3 + 9 y^2 - 5 y)
\][/tex]
becomes:
[tex]\[
-8 y^2 - 9 y + 8 y^3 - 9 y^2 + 5 y
\][/tex]
3. Combine like terms by grouping the coefficients of the like powers of [tex]\( y \)[/tex]:
[tex]\[
(8 y^3) + (-8 y^2 - 9 y^2) + (-9 y + 5 y)
\][/tex]
4. Simplify each group:
- The coefficient of [tex]\( y^3 \)[/tex] is [tex]\( 8 \)[/tex]:
[tex]\[ 8 y^3 \][/tex]
- The coefficient of [tex]\( y^2 \)[/tex] is [tex]\( -8 - 9 \)[/tex]:
[tex]\[ -8 y^2 - 9 y^2 = -17 y^2 \][/tex]
- The coefficient of [tex]\( y \)[/tex] is [tex]\( -9 + 5 \)[/tex]:
[tex]\[ -9 y + 5 y = -4 y \][/tex]
5. Combine these results into the final polynomial:
[tex]\[
8 y^3 - 17 y^2 - 4 y
\][/tex]
Therefore, the result of subtracting the given polynomials is:
[tex]\[
\boxed{8 y^3 - 17 y^2 - 4 y}
\][/tex]
