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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]

Answer :

To find the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex], we need to use the distributive property, also known as the FOIL method for binomials. Here's a step-by-step breakdown:

1. Distribute each term in the first expression by each term in the second expression:

- First, take [tex]\(-2x\)[/tex] and distribute it to both [tex]\(-4x\)[/tex] and [tex]\(-3\)[/tex].
- [tex]\((-2x) \times (-4x) = 8x^2\)[/tex]
- [tex]\((-2x) \times (-3) = 6x\)[/tex]

- Next, take [tex]\(-9y^2\)[/tex] and distribute it to both [tex]\(-4x\)[/tex] and [tex]\(-3\)[/tex].
- [tex]\((-9y^2) \times (-4x) = 36xy^2\)[/tex]
- [tex]\((-9y^2) \times (-3) = 27y^2\)[/tex]

2. Combine all the terms together:

Putting it all together, we have:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]

This expression represents the product of the two binomials, [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex].

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