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Answer :
To solve the problem of finding the product of [tex]\((-2x - 9y^2)\)[/tex] and [tex]\((-4x - 3)\)[/tex], we need to use the distributive property, which involves multiplying each term in the first expression by each term in the second expression. Let's go through the steps:
1. Distribute [tex]\((-2x)\)[/tex]:
- Multiply [tex]\((-2x)\)[/tex] by [tex]\((-4x)\)[/tex]:
[tex]\[
(-2x) \cdot (-4x) = 8x^2
\][/tex]
- Multiply [tex]\((-2x)\)[/tex] by [tex]\((-3)\)[/tex]:
[tex]\[
(-2x) \cdot (-3) = 6x
\][/tex]
2. Distribute [tex]\((-9y^2)\)[/tex]:
- Multiply [tex]\((-9y^2)\)[/tex] by [tex]\((-4x)\)[/tex]:
[tex]\[
(-9y^2) \cdot (-4x) = 36xy^2
\][/tex]
- Multiply [tex]\((-9y^2)\)[/tex] by [tex]\((-3)\)[/tex]:
[tex]\[
(-9y^2) \cdot (-3) = 27y^2
\][/tex]
3. Combine all the results:
Now, we add up all of the terms we calculated:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Therefore, the product of [tex]\((-2x - 9y^2)\)[/tex] and [tex]\((-4x - 3)\)[/tex] is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This matches with one of the given answer choices:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
1. Distribute [tex]\((-2x)\)[/tex]:
- Multiply [tex]\((-2x)\)[/tex] by [tex]\((-4x)\)[/tex]:
[tex]\[
(-2x) \cdot (-4x) = 8x^2
\][/tex]
- Multiply [tex]\((-2x)\)[/tex] by [tex]\((-3)\)[/tex]:
[tex]\[
(-2x) \cdot (-3) = 6x
\][/tex]
2. Distribute [tex]\((-9y^2)\)[/tex]:
- Multiply [tex]\((-9y^2)\)[/tex] by [tex]\((-4x)\)[/tex]:
[tex]\[
(-9y^2) \cdot (-4x) = 36xy^2
\][/tex]
- Multiply [tex]\((-9y^2)\)[/tex] by [tex]\((-3)\)[/tex]:
[tex]\[
(-9y^2) \cdot (-3) = 27y^2
\][/tex]
3. Combine all the results:
Now, we add up all of the terms we calculated:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Therefore, the product of [tex]\((-2x - 9y^2)\)[/tex] and [tex]\((-4x - 3)\)[/tex] is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This matches with one of the given answer choices:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
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