Answer :
We want to subtract the polynomial
[tex]$$
4x^3 + 9xy + 8y
$$[/tex]
by the polynomial
[tex]$$
3x^3 + 5xy - 8y.
$$[/tex]
Step 1: Write the subtraction as follows:
[tex]$$
(4x^3 + 9xy + 8y) - (3x^3 + 5xy - 8y).
$$[/tex]
Step 2: Distribute the negative sign to each term of the second polynomial:
[tex]$$
4x^3 + 9xy + 8y - 3x^3 - 5xy + 8y.
$$[/tex]
Step 3: Combine like terms.
- For the [tex]$x^3$[/tex] terms:
[tex]$$
4x^3 - 3x^3 = x^3.
$$[/tex]
- For the [tex]$xy$[/tex] terms:
[tex]$$
9xy - 5xy = 4xy.
$$[/tex]
- For the [tex]$y$[/tex] terms:
[tex]$$
8y + 8y = 16y.
$$[/tex]
Step 4: Write the final result by combining all the simplified terms:
[tex]$$
x^3 + 4xy + 16y.
$$[/tex]
Thus, the final answer is
[tex]$$
\boxed{x^3+4xy+16y}.
$$[/tex]
This corresponds to option C.
[tex]$$
4x^3 + 9xy + 8y
$$[/tex]
by the polynomial
[tex]$$
3x^3 + 5xy - 8y.
$$[/tex]
Step 1: Write the subtraction as follows:
[tex]$$
(4x^3 + 9xy + 8y) - (3x^3 + 5xy - 8y).
$$[/tex]
Step 2: Distribute the negative sign to each term of the second polynomial:
[tex]$$
4x^3 + 9xy + 8y - 3x^3 - 5xy + 8y.
$$[/tex]
Step 3: Combine like terms.
- For the [tex]$x^3$[/tex] terms:
[tex]$$
4x^3 - 3x^3 = x^3.
$$[/tex]
- For the [tex]$xy$[/tex] terms:
[tex]$$
9xy - 5xy = 4xy.
$$[/tex]
- For the [tex]$y$[/tex] terms:
[tex]$$
8y + 8y = 16y.
$$[/tex]
Step 4: Write the final result by combining all the simplified terms:
[tex]$$
x^3 + 4xy + 16y.
$$[/tex]
Thus, the final answer is
[tex]$$
\boxed{x^3+4xy+16y}.
$$[/tex]
This corresponds to option C.
