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

A) [tex]7x^3 + 14xy[/tex]

B) [tex]x^3 + 4xy[/tex]

C) [tex]7x^3 + 14xy + 16y[/tex]

D) [tex]x^3 + 4xy + 16y[/tex]

Answer :

We start with the expression

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

Step 1. Distribute the subtraction over the second parenthesis:

[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 final polynomial by adding the combined terms:

[tex]$$
x^3 + 4xy + 16y.
$$[/tex]

Thus, the simplified result is

[tex]$$
\boxed{x^3 + 4xy + 16y},
$$[/tex]

which corresponds to option D.

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