Answer :
To find the product [tex]\(( -2x - 9y^2)( -4x - 3)\)[/tex], we will use the distributive property (also known as the FOIL method for binomials). This entails multiplying each term in the first binomial by each term in the second binomial and then combining the results.
1. First, we multiply the first terms of each binomial:
[tex]\[
(-2x) \cdot (-4x) = 8x^2
\][/tex]
2. Next, we multiply the outer terms:
[tex]\[
(-2x) \cdot (-3) = 6x
\][/tex]
3. Then, we multiply the inner terms:
[tex]\[
(-9y^2) \cdot (-4x) = 36xy^2
\][/tex]
4. Lastly, we multiply the last terms of each binomial:
[tex]\[
(-9y^2) \cdot (-3) = 27y^2
\][/tex]
Combining all these products, we get:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Therefore, the correct answer is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the product is:
[tex]\[
\boxed{8x^2 + 6x + 36xy^2 + 27y^2}
\][/tex]
1. First, we multiply the first terms of each binomial:
[tex]\[
(-2x) \cdot (-4x) = 8x^2
\][/tex]
2. Next, we multiply the outer terms:
[tex]\[
(-2x) \cdot (-3) = 6x
\][/tex]
3. Then, we multiply the inner terms:
[tex]\[
(-9y^2) \cdot (-4x) = 36xy^2
\][/tex]
4. Lastly, we multiply the last terms of each binomial:
[tex]\[
(-9y^2) \cdot (-3) = 27y^2
\][/tex]
Combining all these products, we get:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Therefore, the correct answer is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the product is:
[tex]\[
\boxed{8x^2 + 6x + 36xy^2 + 27y^2}
\][/tex]
