Answer :
We start with the expression:
$$
\left(4x^3 + 9xy + 8y\right) - \left(3x^3 + 5xy - 8y\right).
$$
**Step 1: Distribute the subtraction**
Subtracting the second polynomial means we change the signs of each term in the second polynomial:
$$
4x^3 + 9xy + 8y - 3x^3 - 5xy + 8y.
$$
**Step 2: Combine like terms**
- For the \(x^3\) terms:
$$
4x^3 - 3x^3 = x^3.
$$
- For the \(xy\) terms:
$$
9xy - 5xy = 4xy.
$$
- For the \(y\) terms:
$$
8y + 8y = 16y.
$$
**Step 3: Write the simplified expression**
Putting it all together, we obtain:
$$
x^3 + 4xy + 16y.
$$
Thus, the correct answer is:
$$
\boxed{x^3 + 4xy + 16y}.
$$
$$
\left(4x^3 + 9xy + 8y\right) - \left(3x^3 + 5xy - 8y\right).
$$
**Step 1: Distribute the subtraction**
Subtracting the second polynomial means we change the signs of each term in the second polynomial:
$$
4x^3 + 9xy + 8y - 3x^3 - 5xy + 8y.
$$
**Step 2: Combine like terms**
- For the \(x^3\) terms:
$$
4x^3 - 3x^3 = x^3.
$$
- For the \(xy\) terms:
$$
9xy - 5xy = 4xy.
$$
- For the \(y\) terms:
$$
8y + 8y = 16y.
$$
**Step 3: Write the simplified expression**
Putting it all together, we obtain:
$$
x^3 + 4xy + 16y.
$$
Thus, the correct answer is:
$$
\boxed{x^3 + 4xy + 16y}.
$$
