College

What is the product?

[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 the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex], we need to apply the distributive property, also known as the FOIL method (First, Outer, Inner, Last). Here's how you do it step by step:

1. First Terms: Multiply the first terms from each binomial:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]

2. Outer Terms: Multiply the outer terms:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]

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

4. Last Terms: Multiply the last terms from each binomial:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]

Now, combine all the terms together to form the final expression:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]

The correct product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]

This matches the choice [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex] from the given options.