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Answer :
Sure! Let's find the product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] using distributive property:
1. Distribute [tex]\(-2x\)[/tex] across the second set of parentheses:
- 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] across the second set of parentheses:
- 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 together:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
The result of the multiplication 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] across the second set of parentheses:
- 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] across the second set of parentheses:
- 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 together:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
The result of the multiplication 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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