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Answer :
To find the product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex], we will use the distributive property, which involves distributing each term in the first polynomial to each term in the second polynomial.
Let's break it down step-by-step:
1. Distribute the [tex]\(-2x\)[/tex] term:
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\((-2x) \times (-4x) = 8x^2\)[/tex]
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\((-2x) \times (-3) = 6x\)[/tex]
2. Distribute the [tex]\(-9y^2\)[/tex] term:
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\((-9y^2) \times (-4x) = 36xy^2\)[/tex]
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\((-9y^2) \times (-3) = 27y^2\)[/tex]
3. Combine all the results:
- [tex]\[8x^2 + 6x + 36xy^2 + 27y^2\][/tex]
Therefore, after distributing and combining all the terms, the product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is:
[tex]\[8x^2 + 6x + 36xy^2 + 27y^2\][/tex]
So, the correct option is:
[tex]\[8x^2 + 6x + 36xy^2 + 27y^2\][/tex]
Let's break it down step-by-step:
1. Distribute the [tex]\(-2x\)[/tex] term:
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\((-2x) \times (-4x) = 8x^2\)[/tex]
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\((-2x) \times (-3) = 6x\)[/tex]
2. Distribute the [tex]\(-9y^2\)[/tex] term:
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\((-9y^2) \times (-4x) = 36xy^2\)[/tex]
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\((-9y^2) \times (-3) = 27y^2\)[/tex]
3. Combine all the results:
- [tex]\[8x^2 + 6x + 36xy^2 + 27y^2\][/tex]
Therefore, after distributing and combining all the terms, the product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is:
[tex]\[8x^2 + 6x + 36xy^2 + 27y^2\][/tex]
So, the correct option is:
[tex]\[8x^2 + 6x + 36xy^2 + 27y^2\][/tex]
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