To subtract the given polynomials, we start by distributing the negative sign through the second polynomial and then combine like terms.
The given polynomials are:
[tex]\[
\left(8 y^3 + 4 y^2 - y - 3\right) - \left(y^2 - 8 y + 5\right)
\][/tex]
First, distribute the negative sign through the second polynomial:
[tex]\[
8 y^3 + 4 y^2 - y - 3 - y^2 + 8 y - 5
\][/tex]
Now, combine like terms by grouping them together:
[tex]\[
8 y^3 + (4 y^2 - y^2) + (-y + 8 y) + (-3 - 5)
\][/tex]
Next, perform the operations within each group:
[tex]\[
8 y^3 + 3 y^2 + 7 y - 8
\][/tex]
Thus, the simplified difference of the given polynomials is:
[tex]\[
8 y^3 + 3 y^2 + 7 y - 8
\][/tex]
The difference is [tex]\( 8 y^3 + 3 y^2 + 7 y - 8 \)[/tex] .
