High School

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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 :

To find the product [tex]\(\left(-2x - 9y^2\right)(-4x - 3)\)[/tex], we'll use the distributive property to multiply each term in the first parenthesis by each term in the second parenthesis.

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

2. Multiply the first term by the second term:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]

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

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

Now, we will combine all the resulting terms:

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

This is the expanded form of the product, which matches the expression [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex]. So, the correct choice from the options is:

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

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