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]

Let's solve this problem step-by-step to find the product of the expression [tex]$(-2x - 9y^2)(-4x - 3)$[/tex].

1. Distribute Each Term:
We will use the distributive property to multiply each term in the first parenthesis by each term in the second parenthesis.

2. Multiply The Terms:
- First, multiply [tex]$-2x$[/tex] by each term in the second parenthesis:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
- Next, multiply [tex]$-9y^2$[/tex] by each term in the second parenthesis:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]

3. Combine the Results:
Add all the results from the steps above together:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]

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

Finally, matching this expression with the given options, we find that it corresponds to:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]

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

Therefore, the correct choice is the third option.

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 :

Other Questions

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]