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------------------------------------------------ Simplify the expression:

[tex]\[

(-2x - 9y^2)(-4x - 3)

\][/tex]

Choose the correct simplified form:

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]

Sure! Let's solve the expression [tex]$(-2x - 9y^2)(-4x - 3)$[/tex] step-by-step by distributing the terms.

1. Apply the distributive property: Distribute each term in the first set of parentheses to each term in the second set of parentheses.

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

2. Multiply each term:
- Multiply [tex]$(-2x)(-4x)$[/tex]:

[tex]\[
(-2x)(-4x) = 8x^2
\][/tex]

- Multiply [tex]$(-2x)(-3)$[/tex]:

[tex]\[
(-2x)(-3) = 6x
\][/tex]

- Multiply [tex]$(-9y^2)(-4x)$[/tex]:

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

- Multiply [tex]$(-9y^2)(-3)$[/tex]:

[tex]\[
(-9y^2)(-3) = 27y^2
\][/tex]

3. Combine all the results:

Adding these results together, we have:

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

So, the simplified result of the expression is:

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

This is the expanded and simplified form of the original expression given.