College

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 [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex], we can use the distributive property, also known as the FOIL method for binomials (First, Outer, Inner, Last). Let's expand the expression step-by-step:

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

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

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

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

Finally, combine all these terms to get the expanded product:

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

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

From the provided options, the correct one is:

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