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What is the product of the 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 :

We want to multiply the two binomials:

[tex]$$
(-2x - 9y^2)(-4x - 3)
$$[/tex]

Step 1. Multiply each term in the first binomial by each term in the second binomial.

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

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

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

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

Step 2. Combine all these products to form the final expression:

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

Thus, the product of the binomials is:

[tex]$$
\boxed{8x^2 + 6x + 36xy^2 + 27y^2}
$$[/tex]

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