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Answer :
To solve the multiplication of the polynomials [tex]\((9x + 7)(3x^2 + 5x - 1)\)[/tex], we'll perform the operation by distributing each term in the first polynomial to every term in the second polynomial and then combine like terms.
1. Distribute [tex]\(9x\)[/tex] to each term in [tex]\((3x^2 + 5x - 1)\)[/tex]:
- [tex]\(9x \cdot 3x^2 = 27x^3\)[/tex]
- [tex]\(9x \cdot 5x = 45x^2\)[/tex]
- [tex]\(9x \cdot (-1) = -9x\)[/tex]
2. Distribute [tex]\(7\)[/tex] to each term in [tex]\((3x^2 + 5x - 1)\)[/tex]:
- [tex]\(7 \cdot 3x^2 = 21x^2\)[/tex]
- [tex]\(7 \cdot 5x = 35x\)[/tex]
- [tex]\(7 \cdot (-1) = -7\)[/tex]
3. Combine all terms:
- Combine the [tex]\(x^3\)[/tex] terms: [tex]\(27x^3\)[/tex]
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(45x^2 + 21x^2 = 66x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-9x + 35x = 26x\)[/tex]
- Constant term: [tex]\(-7\)[/tex]
4. Write the final expression:
[tex]\[
27x^3 + 66x^2 + 26x - 7
\][/tex]
Therefore, the correct product of [tex]\((9x + 7)(3x^2 + 5x - 1)\)[/tex] is [tex]\(\boxed{27x^3 + 66x^2 + 26x - 7}\)[/tex].
1. Distribute [tex]\(9x\)[/tex] to each term in [tex]\((3x^2 + 5x - 1)\)[/tex]:
- [tex]\(9x \cdot 3x^2 = 27x^3\)[/tex]
- [tex]\(9x \cdot 5x = 45x^2\)[/tex]
- [tex]\(9x \cdot (-1) = -9x\)[/tex]
2. Distribute [tex]\(7\)[/tex] to each term in [tex]\((3x^2 + 5x - 1)\)[/tex]:
- [tex]\(7 \cdot 3x^2 = 21x^2\)[/tex]
- [tex]\(7 \cdot 5x = 35x\)[/tex]
- [tex]\(7 \cdot (-1) = -7\)[/tex]
3. Combine all terms:
- Combine the [tex]\(x^3\)[/tex] terms: [tex]\(27x^3\)[/tex]
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(45x^2 + 21x^2 = 66x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-9x + 35x = 26x\)[/tex]
- Constant term: [tex]\(-7\)[/tex]
4. Write the final expression:
[tex]\[
27x^3 + 66x^2 + 26x - 7
\][/tex]
Therefore, the correct product of [tex]\((9x + 7)(3x^2 + 5x - 1)\)[/tex] is [tex]\(\boxed{27x^3 + 66x^2 + 26x - 7}\)[/tex].
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