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Answer :
Let's solve the problem by expanding and simplifying the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex].
1. Distribute each term in the first polynomial to each term in the second polynomial.
2. Start with [tex]\(-2x\)[/tex]:
- 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].
3. Now, distribute [tex]\( -9y^2\)[/tex]:
- 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].
4. Combine all the terms:
- [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
After combining like terms, the expression becomes: [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
Thus, the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
Hence, the answer is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
1. Distribute each term in the first polynomial to each term in the second polynomial.
2. Start with [tex]\(-2x\)[/tex]:
- 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].
3. Now, distribute [tex]\( -9y^2\)[/tex]:
- 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].
4. Combine all the terms:
- [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
After combining like terms, the expression becomes: [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
Thus, the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
Hence, the answer is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
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