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Answer :
Sure! Let's find the product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] step by step:
1. Identify the terms of the polynomials:
- The first expression [tex]\(-2x - 9y^2\)[/tex] has terms [tex]\(-2x\)[/tex] and [tex]\(-9y^2\)[/tex].
- The second expression [tex]\(-4x - 3\)[/tex] has terms [tex]\(-4x\)[/tex] and [tex]\(-3\)[/tex].
2. Use the distributive property to expand:
- Multiply each term in the first expression by each term in the second expression, and then add the results together.
3. Multiply the terms:
- [tex]\(-2x \times -4x = 8x^2\)[/tex]
- [tex]\(-2x \times -3 = 6x\)[/tex]
- [tex]\(-9y^2 \times -4x = 36xy^2\)[/tex]
- [tex]\(-9y^2 \times -3 = 27y^2\)[/tex]
4. Combine all the products:
- Add up all the results: [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
So, the final expanded form of the product is:
[tex]\[8x^2 + 36xy^2 + 6x + 27y^2\][/tex]
Therefore, the correct choice from the given options is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
1. Identify the terms of the polynomials:
- The first expression [tex]\(-2x - 9y^2\)[/tex] has terms [tex]\(-2x\)[/tex] and [tex]\(-9y^2\)[/tex].
- The second expression [tex]\(-4x - 3\)[/tex] has terms [tex]\(-4x\)[/tex] and [tex]\(-3\)[/tex].
2. Use the distributive property to expand:
- Multiply each term in the first expression by each term in the second expression, and then add the results together.
3. Multiply the terms:
- [tex]\(-2x \times -4x = 8x^2\)[/tex]
- [tex]\(-2x \times -3 = 6x\)[/tex]
- [tex]\(-9y^2 \times -4x = 36xy^2\)[/tex]
- [tex]\(-9y^2 \times -3 = 27y^2\)[/tex]
4. Combine all the products:
- Add up all the results: [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
So, the final expanded form of the product is:
[tex]\[8x^2 + 36xy^2 + 6x + 27y^2\][/tex]
Therefore, the correct choice from the given options is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
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