College

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 :

Let's find the product of the given expressions: [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex].

To multiply these two expressions together, you will apply the distributive property, often referred to as FOIL (First, Outside, Inside, Last) for binomials.

1. First Terms: Multiply the first terms of each binomial:
[tex]\[
(-2x) \cdot (-4x) = 8x^2
\][/tex]

2. Outside Terms: Multiply the outer terms of the binomials:
[tex]\[
(-2x) \cdot (-3) = 6x
\][/tex]

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

4. Last Terms: Multiply the last terms of each binomial:
[tex]\[
(-9y^2) \cdot (-3) = 27y^2
\][/tex]

Now, combine all the results:

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

So the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] simplifies to:

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

Among the given choices, this matches:

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

Therefore, this is the correct product of the expressions.