College

What is the product of [tex](-2x - 8y^2)(-4x - 3)[/tex]?

A. [tex]-8x^2 - 6x - 36y^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 solve the problem step-by-step by simplifying [tex]\((-2x - 8y^2)(-4x - 3)\)[/tex] using the distributive property.

1. Distribute [tex]\(-2x\)[/tex] to each term in [tex]\((-4x - 3)\)[/tex]:

[tex]\[
-2x \times -4x = 8x^2
\][/tex]

[tex]\[
-2x \times -3 = 6x
\][/tex]

So, distributing [tex]\(-2x\)[/tex] gives us [tex]\(8x^2 + 6x\)[/tex].

2. Distribute [tex]\(-8y^2\)[/tex] to each term in [tex]\((-4x - 3)\)[/tex]:

[tex]\[
-8y^2 \times -4x = 32xy^2
\][/tex]

[tex]\[
-8y^2 \times -3 = 24y^2
\][/tex]

So, distributing [tex]\(-8y^2\)[/tex] gives us [tex]\(32xy^2 + 24y^2\)[/tex].

3. Combine all the terms together:

When you put together all the terms from the distribution steps, you get:

[tex]\[
8x^2 + 6x + 32xy^2 + 24y^2
\][/tex]

The final simplified product of the expression [tex]\((-2x - 8y^2)(-4x - 3)\)[/tex] is [tex]\(8x^2 + 6x + 32xy^2 + 24y^2\)[/tex].