College

What is the product of the following 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 :

We start with the product:

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

To find the result, we use the distributive property (also known as the FOIL method):

1. Multiply [tex]$-2x$[/tex] by [tex]$-4x$[/tex]:
[tex]$$
(-2x)(-4x) = 8x^2
$$[/tex]

2. Multiply [tex]$-2x$[/tex] by [tex]$-3$[/tex]:
[tex]$$
(-2x)(-3) = 6x
$$[/tex]

3. Multiply [tex]$-9y^2$[/tex] by [tex]$-4x$[/tex]:
[tex]$$
(-9y^2)(-4x) = 36xy^2
$$[/tex]

4. Multiply [tex]$-9y^2$[/tex] by [tex]$-3$[/tex]:
[tex]$$
(-9y^2)(-3) = 27y^2
$$[/tex]

Finally, combine all these products:

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

This is the expanded and simplified product.

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