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Subtract: [tex]\left(4x^3 + 9xy + 8y\right) - \left(3x^3 + 5xy - 8y\right)[/tex]

A) [tex]x^3 + 4xy + 16y[/tex]
B) [tex]7x^3 + 14xy + 16y[/tex]
C) [tex]x^3 + 4xy[/tex]
D) [tex]7x^3 + 14xy[/tex]

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]

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