Answer :
Let's solve the problem of multiplying [tex]\((8x + 9)(3x^2 + x - 1)\)[/tex] step by step without referencing any erroneous code or unnecessary information.
### Step-by-Step Multiplication:
1. Distribute the [tex]\(8x\)[/tex] to each term inside the parentheses [tex]\((3x^2 + x - 1)\)[/tex]:
- [tex]\(8x \cdot 3x^2 = 24x^3\)[/tex]
- [tex]\(8x \cdot x = 8x^2\)[/tex]
- [tex]\(8x \cdot (-1) = -8x\)[/tex]
2. Distribute the [tex]\(9\)[/tex] to each term inside the parentheses [tex]\((3x^2 + x - 1)\)[/tex]:
- [tex]\(9 \cdot 3x^2 = 27x^2\)[/tex]
- [tex]\(9 \cdot x = 9x\)[/tex]
- [tex]\(9 \cdot (-1) = -9\)[/tex]
3. Combine all the results:
- From [tex]\(8x\)[/tex]: [tex]\(24x^3 + 8x^2 - 8x\)[/tex]
- From [tex]\(9\)[/tex]: [tex]\(27x^2 + 9x - 9\)[/tex]
4. Add like terms:
- For [tex]\(x^3\)[/tex] terms: [tex]\(24x^3\)[/tex] (no other [tex]\(x^3\)[/tex] terms)
- For [tex]\(x^2\)[/tex] terms: [tex]\(8x^2 + 27x^2 = 35x^2\)[/tex]
- For [tex]\(x\)[/tex] terms: [tex]\(-8x + 9x = 1x\)[/tex]
- Constant term: [tex]\(-9\)[/tex]
5. The final expanded form is:
[tex]\[
24x^3 + 35x^2 + x - 9
\][/tex]
So, the correct answer is [tex]\(24x^3 + 35x^2 + x - 9\)[/tex].
### Step-by-Step Multiplication:
1. Distribute the [tex]\(8x\)[/tex] to each term inside the parentheses [tex]\((3x^2 + x - 1)\)[/tex]:
- [tex]\(8x \cdot 3x^2 = 24x^3\)[/tex]
- [tex]\(8x \cdot x = 8x^2\)[/tex]
- [tex]\(8x \cdot (-1) = -8x\)[/tex]
2. Distribute the [tex]\(9\)[/tex] to each term inside the parentheses [tex]\((3x^2 + x - 1)\)[/tex]:
- [tex]\(9 \cdot 3x^2 = 27x^2\)[/tex]
- [tex]\(9 \cdot x = 9x\)[/tex]
- [tex]\(9 \cdot (-1) = -9\)[/tex]
3. Combine all the results:
- From [tex]\(8x\)[/tex]: [tex]\(24x^3 + 8x^2 - 8x\)[/tex]
- From [tex]\(9\)[/tex]: [tex]\(27x^2 + 9x - 9\)[/tex]
4. Add like terms:
- For [tex]\(x^3\)[/tex] terms: [tex]\(24x^3\)[/tex] (no other [tex]\(x^3\)[/tex] terms)
- For [tex]\(x^2\)[/tex] terms: [tex]\(8x^2 + 27x^2 = 35x^2\)[/tex]
- For [tex]\(x\)[/tex] terms: [tex]\(-8x + 9x = 1x\)[/tex]
- Constant term: [tex]\(-9\)[/tex]
5. The final expanded form is:
[tex]\[
24x^3 + 35x^2 + x - 9
\][/tex]
So, the correct answer is [tex]\(24x^3 + 35x^2 + x - 9\)[/tex].
