High School

What is the product of the expression?

[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 :

To find the product of
[tex]$$(-2x - 9y^2)(-4x - 3),$$[/tex]
we can multiply each term in the first parenthesis by each term in the second parenthesis.

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, combine all the obtained terms:
[tex]$$8x^2 + 6x + 36xy^2 + 27y^2.$$[/tex]

Thus, the product is
[tex]$$8x^2 + 6x + 36xy^2 + 27y^2,$$[/tex]
which corresponds to option 3.