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What is the product?

1. [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 :

Sure! Let's find the product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] by using the distributive property, also known as the FOIL method for binomials.

Step 1: Distribute each term

1. Multiply the first term in the first binomial by each term in the second binomial:
- [tex]\((-2x) \cdot (-4x) = 8x^2\)[/tex]
- [tex]\((-2x) \cdot (-3) = 6x\)[/tex]

2. Multiply the second term in the first binomial by each term in the second binomial:
- [tex]\((-9y^2) \cdot (-4x) = 36xy^2\)[/tex]
- [tex]\((-9y^2) \cdot (-3) = 27y^2\)[/tex]

Step 2: Combine all the results

Now, we combine all of these products:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]

This is the expanded expression.

Conclusion

From the original options provided, the correct choice is:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]

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