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Answer :
To determine the product [tex]\((\left(-2 x-9 y^2\right)(-4 x-3)\)[/tex], let's break down the multiplication step-by-step.
1. Distribute [tex]\(-2x\)[/tex]:
- Multiply [tex]\(-2x\)[/tex] by each term inside the second set of parentheses:
- [tex]\(-2x \times -4x = 8x^2\)[/tex]
- [tex]\(-2x \times -3 = 6x\)[/tex]
2. Distribute [tex]\(-9y^2\)[/tex]:
- Multiply [tex]\(-9y^2\)[/tex] by each term inside the second set of parentheses:
- [tex]\(-9y^2 \times -4x = 36xy^2\)[/tex]
- [tex]\(-9y^2 \times -3 = 27y^2\)[/tex]
3. Combine like terms:
- Combine the results from both distributions:
[tex]\[8x^2 + 6x + 36xy^2 + 27y^2\][/tex]
So, the product of the expression [tex]\(\left(-2 x-9 y^2\right)(-4 x-3)\)[/tex] is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
Therefore, the correct choice from the given options is:
[tex]\[ \boxed{8x^2 + 6x + 36xy^2 + 27y^2} \][/tex]
1. Distribute [tex]\(-2x\)[/tex]:
- Multiply [tex]\(-2x\)[/tex] by each term inside the second set of parentheses:
- [tex]\(-2x \times -4x = 8x^2\)[/tex]
- [tex]\(-2x \times -3 = 6x\)[/tex]
2. Distribute [tex]\(-9y^2\)[/tex]:
- Multiply [tex]\(-9y^2\)[/tex] by each term inside the second set of parentheses:
- [tex]\(-9y^2 \times -4x = 36xy^2\)[/tex]
- [tex]\(-9y^2 \times -3 = 27y^2\)[/tex]
3. Combine like terms:
- Combine the results from both distributions:
[tex]\[8x^2 + 6x + 36xy^2 + 27y^2\][/tex]
So, the product of the expression [tex]\(\left(-2 x-9 y^2\right)(-4 x-3)\)[/tex] is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
Therefore, the correct choice from the given options is:
[tex]\[ \boxed{8x^2 + 6x + 36xy^2 + 27y^2} \][/tex]
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