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What is the product?

[tex]
\[
(-2x - 9y^2)(-4x - 3)
\]
[/tex]

A. [tex]\(-8x^2 - 6x - 36xy^2 - 27y^2\)[/tex]

B. [tex]\(-14x^2 - 36xy^2 + 27y^2\)[/tex]

C. [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex]

D. [tex]\(14x^2 + 36xy^2 + 27y^2\)[/tex]

Answer :

To find the product of
[tex]$$
(-2x - 9y^2)(-4x - 3),
$$[/tex]
we multiply each term in the first parenthesis by each term in the second parenthesis.

1. Multiply the first terms:
[tex]$$
(-2x) \cdot (-4x) = 8x^2
$$[/tex]

2. Multiply the outer terms:
[tex]$$
(-2x) \cdot (-3) = 6x
$$[/tex]

3. Multiply the inner terms:
[tex]$$
(-9y^2) \cdot (-4x) = 36xy^2
$$[/tex]

4. Multiply the last terms:
[tex]$$
(-9y^2) \cdot (-3) = 27y^2
$$[/tex]

Now, add all the like terms together:
[tex]$$
8x^2 + 6x + 36xy^2 + 27y^2.
$$[/tex]

Thus, the product is:
[tex]$$
8x^2 + 6x + 36xy^2 + 27y^2.
$$[/tex]

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