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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 the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex], we will expand the expression using the distributive property, sometimes called the FOIL method for binomials (First, Outside, Inside, Last). Here’s how you can do it step by step:

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

2. Multiply the Outside terms:
[tex]\((-2x) \times (-3) = 6x\)[/tex]

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

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

Now, combine all these results to write the expanded expression:

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

This is the expanded form of the given product. Therefore, the correct answer is:

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

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