Answer :
To find the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex], we can use the distributive property, also known as the FOIL method when working with binomials. This involves multiplying each term in the first expression by each term in the second expression. Let’s go through it step by step:
1. First, multiply the first terms from each binomial:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
2. Next, multiply the outer terms:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
3. Then, multiply the inner terms:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
4. Finally, multiply the last terms from each binomial:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
Now, add all these products together to get the final expression:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the expanded product is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This matches the choice:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
1. First, multiply the first terms from each binomial:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
2. Next, multiply the outer terms:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
3. Then, multiply the inner terms:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
4. Finally, multiply the last terms from each binomial:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
Now, add all these products together to get the final expression:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the expanded product is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This matches the choice:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
