Answer :
We want to subtract
[tex]$$
(4x^3 + 9xy + 8y) - (3x^3 + 5xy - 8y).
$$[/tex]
Step 1. Distribute the negative sign
Subtracting the second expression is equivalent to changing the signs of its terms:
[tex]$$
4x^3 + 9xy + 8y - 3x^3 - 5xy + 8y.
$$[/tex]
Step 2. Combine like terms
1. For the [tex]$x^3$[/tex] terms:
[tex]$$
4x^3 - 3x^3 = x^3.
$$[/tex]
2. For the [tex]$xy$[/tex] terms:
[tex]$$
9xy - 5xy = 4xy.
$$[/tex]
3. For the [tex]$y$[/tex] terms:
[tex]$$
8y + 8y = 16y.
$$[/tex]
Step 3. Write the simplified expression
After combining the like terms, the final expression is
[tex]$$
x^3 + 4xy + 16y.
$$[/tex]
Thus, the correct answer is:
[tex]$$
\boxed{x^3 + 4xy + 16y}.
$$[/tex]
[tex]$$
(4x^3 + 9xy + 8y) - (3x^3 + 5xy - 8y).
$$[/tex]
Step 1. Distribute the negative sign
Subtracting the second expression is equivalent to changing the signs of its terms:
[tex]$$
4x^3 + 9xy + 8y - 3x^3 - 5xy + 8y.
$$[/tex]
Step 2. Combine like terms
1. For the [tex]$x^3$[/tex] terms:
[tex]$$
4x^3 - 3x^3 = x^3.
$$[/tex]
2. For the [tex]$xy$[/tex] terms:
[tex]$$
9xy - 5xy = 4xy.
$$[/tex]
3. For the [tex]$y$[/tex] terms:
[tex]$$
8y + 8y = 16y.
$$[/tex]
Step 3. Write the simplified expression
After combining the like terms, the final expression is
[tex]$$
x^3 + 4xy + 16y.
$$[/tex]
Thus, the correct answer is:
[tex]$$
\boxed{x^3 + 4xy + 16y}.
$$[/tex]
