College

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

D. [tex]14x^2 + 36xy^2 + 27y^2[/tex]

Answer :

We want to multiply

[tex]$$
\left(-2x - 9y^2\right) \left(-4x - 3\right).
$$[/tex]

To do this, we use the distributive property by multiplying each term in the first factor by each term in the second factor.

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

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

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

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

Now, add all the products together:

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

Thus, the final product is

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