College

Multiply: [tex] (9x+8)(3x^2+x-1) [/tex]

A. [tex] 3x^2 + 10x + 7 [/tex]

B. [tex] 27x^3 + 33x^2 - x - 8 [/tex]

C. [tex] 27x^3 + 33x^2 + 17x + 8 [/tex]

D. [tex] 27x^3 + 9x^2 - 8 [/tex]

Answer :

Sure! Let's solve the problem of multiplying the polynomials [tex]\((9x + 8)\)[/tex] and [tex]\((3x^2 + x - 1)\)[/tex] step-by-step.

Step 1: Distribute each term in the first polynomial by each term in the second polynomial.

To start, distribute [tex]\(9x\)[/tex] across the second polynomial:

1. [tex]\(9x \cdot 3x^2 = 27x^3\)[/tex]
2. [tex]\(9x \cdot x = 9x^2\)[/tex]
3. [tex]\(9x \cdot (-1) = -9x\)[/tex]

Next, distribute [tex]\(8\)[/tex] across the second polynomial:

1. [tex]\(8 \cdot 3x^2 = 24x^2\)[/tex]
2. [tex]\(8 \cdot x = 8x\)[/tex]
3. [tex]\(8 \cdot (-1) = -8\)[/tex]

Step 2: Combine all the terms.

Now, combine all the results from the distribution:

- [tex]\(27x^3\)[/tex] (from [tex]\(9x \cdot 3x^2\)[/tex])
- [tex]\(9x^2 + 24x^2 = 33x^2\)[/tex] (from [tex]\(9x \cdot x\)[/tex] and [tex]\(8 \cdot 3x^2\)[/tex])
- [tex]\(-9x + 8x = -x\)[/tex] (from [tex]\(9x \cdot (-1)\)[/tex] and [tex]\(8 \cdot x\)[/tex])
- [tex]\(-8\)[/tex] (from [tex]\(8 \cdot (-1)\)[/tex])

Final Result

Thus, combining all these terms, we have the resulting polynomial:

[tex]\[ 27x^3 + 33x^2 - x - 8 \][/tex]

This is the expanded and combined expression from multiplying [tex]\((9x + 8)\)[/tex] by [tex]\((3x^2 + x - 1)\)[/tex].