Answer :
To find the product [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex], we can expand the expression using the distributive property (also known as the FOIL method for binomials).
Let's expand step by step:
1. Multiply [tex]\(-2x\)[/tex] by each term in the second expression:
[tex]\[
-2x \cdot (-4x) = 8x^2
\][/tex]
[tex]\[
-2x \cdot (-3) = 6x
\][/tex]
2. Multiply [tex]\(-9y^2\)[/tex] by each term in the second expression:
[tex]\[
-9y^2 \cdot (-4x) = 36xy^2
\][/tex]
[tex]\[
-9y^2 \cdot (-3) = 27y^2
\][/tex]
3. Combine all the terms:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Therefore, the expanded product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This matches one of the provided options:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, this is the correct answer.
Let's expand step by step:
1. Multiply [tex]\(-2x\)[/tex] by each term in the second expression:
[tex]\[
-2x \cdot (-4x) = 8x^2
\][/tex]
[tex]\[
-2x \cdot (-3) = 6x
\][/tex]
2. Multiply [tex]\(-9y^2\)[/tex] by each term in the second expression:
[tex]\[
-9y^2 \cdot (-4x) = 36xy^2
\][/tex]
[tex]\[
-9y^2 \cdot (-3) = 27y^2
\][/tex]
3. Combine all the terms:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Therefore, the expanded product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This matches one of the provided options:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, this is the correct answer.
