Answer :
Sure! Let's find the product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] by using the distributive property, often called FOIL for multiplying two binomials.
### Step-by-Step Solution:
1. Multiply the first terms:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
2. Multiply the outer terms:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
3. Multiply the inner terms:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
4. Multiply the last terms:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
5. Combine all the products:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This matches the third option provided in the question list.
### Step-by-Step Solution:
1. Multiply the first terms:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
2. Multiply the outer terms:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
3. Multiply the inner terms:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
4. Multiply the last terms:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
5. Combine all the products:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This matches the third option provided in the question list.
