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------------------------------------------------ What is the product?

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

Let's find the product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] by expanding it step by step.

1. Distribute each term in the first parenthesis to each term in the second parenthesis:

- Multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]

- Multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]

- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]

- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]

2. Combine all the terms we've found:

[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]

So, the expanded form of the expression is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].

The correct answer is the option [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].