High School

What is the product of the expression?

[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 :

To find the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex], we will follow these steps to multiply the expressions:

1. Use the distributive property: This property lets us multiply each term in the first parentheses by each term in the second.

2. Multiply each pair of terms:
- First, multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-2x) \cdot (-4x) = 8x^2
\][/tex]
- Next, multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-2x) \cdot (-3) = 6x
\][/tex]
- Then, multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-9y^2) \cdot (-4x) = 36xy^2
\][/tex]
- Finally, multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-9y^2) \cdot (-3) = 27y^2
\][/tex]

3. Add all the results together:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]

So, the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is [tex]\(\boxed{8x^2 + 6x + 36xy^2 + 27y^2}\)[/tex].