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What is the product of the following expression?

[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]

Answer :

Sure, let's solve the expression step-by-step:

We need to find the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex].

1. Distribute [tex]\(-2x\)[/tex] to each term in [tex]\((-4x - 3)\)[/tex]:

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

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

2. Distribute [tex]\(-9y^2\)[/tex] to each term in [tex]\((-4x - 3)\)[/tex]:

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

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

3. Combine all the products:

Combining all these terms, we get:

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

So, the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is [tex]\(8x^2 + 36xy^2 + 6x + 27y^2\)[/tex].

Therefore, the correct answer is:

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

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