College

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 :

Sure! Let's solve the problem step by step.

We need to find the product of the following expression:

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

We'll do this by distributing each term in the first binomial over each term in the second binomial.

1. Distribute [tex]\(-2x\)[/tex]:

[tex]\[
(-2x) \cdot (-4x) = 8x^2
\][/tex]

[tex]\[
(-2x) \cdot (-3) = 6x
\][/tex]

2. Distribute [tex]\(-9y^2\)[/tex]:

[tex]\[
(-9y^2) \cdot (-4x) = 36xy^2
\][/tex]

[tex]\[
(-9y^2) \cdot (-3) = 27y^2
\][/tex]

3. Combine all the terms:

The resulting expression after distribution and simplifying is:

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

Looking at the options provided:

- [tex]\(-8x^2 - 6x - 36xy^2 - 27y^2\)[/tex]
- [tex]\(-14x^2 - 36xy^2 + 27y^2\)[/tex]
- [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex]
- [tex]\(14x^2 + 36xy^2 + 27y^2\)[/tex]

The correct product based on our calculations is:

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

So, the correct choice is:

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