Answer :
To find the product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex], we need to apply the distributive property, also known as the FOIL method for binomials, which stands for First, Outer, Inner, Last. Here's how it works step-by-step:
1. First: Multiply the first terms of each binomial:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
2. Outer: Multiply the outer terms:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
3. Inner: Multiply the inner terms:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
4. Last: Multiply the last terms of each binomial:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
Now, combine all these results together:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Therefore, the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This result matches one of the given answer choices:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
1. First: Multiply the first terms of each binomial:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
2. Outer: Multiply the outer terms:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
3. Inner: Multiply the inner terms:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
4. Last: Multiply the last terms of each binomial:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
Now, combine all these results together:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Therefore, the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This result matches one of the given answer choices:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
