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------------------------------------------------ What is the product of the following expression?

[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 :

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

To solve this, we'll use the distributive property, also known as the FOIL method in the context of multiplying binomials:

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

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

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

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

Now, add all these results together to get the final expression:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]

So, the product of the given expression is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]