College

What is the product of the following 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 + 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 will use the distributive property, which involves multiplying each term in the first parentheses by each term in the second parentheses. Let's break it down step-by-step:

1. Distribute [tex]\(-2x\)[/tex] to both terms in the second parentheses:
- [tex]\(-2x \times -4x = 8x^2\)[/tex]
- [tex]\(-2x \times -3 = 6x\)[/tex]

2. Distribute [tex]\(-9y^2\)[/tex] to both terms in the second parentheses:
- [tex]\(-9y^2 \times -4x = 36xy^2\)[/tex]
- [tex]\(-9y^2 \times -3 = 27y^2\)[/tex]

3. Combine all the results:
- From step 1, we have [tex]\(8x^2\)[/tex] and [tex]\(6x\)[/tex].
- From step 2, we have [tex]\(36xy^2\)[/tex] and [tex]\(27y^2\)[/tex].

So, when you put them all together, you get the product:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]

This matches the option: [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].