Answer :
To multiply the polynomials [tex]\((8x^2 + 6x + 8)(6x - 5)\)[/tex], we'll distribute each term in the first polynomial by each term in the second polynomial and then combine like terms at the end. Here’s how you can do it step-by-step:
1. Multiply each term in [tex]\((8x^2 + 6x + 8)\)[/tex] by [tex]\(6x\)[/tex]:
- [tex]\(8x^2 \times 6x = 48x^3\)[/tex]
- [tex]\(6x \times 6x = 36x^2\)[/tex]
- [tex]\(8 \times 6x = 48x\)[/tex]
2. Multiply each term in [tex]\((8x^2 + 6x + 8)\)[/tex] by [tex]\(-5\)[/tex]:
- [tex]\(8x^2 \times -5 = -40x^2\)[/tex]
- [tex]\(6x \times -5 = -30x\)[/tex]
- [tex]\(8 \times -5 = -40\)[/tex]
3. Combine all the results from steps 1 and 2:
- The [tex]\(x^3\)[/tex] term: [tex]\(48x^3\)[/tex]
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(36x^2 - 40x^2 = -4x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(48x - 30x = 18x\)[/tex]
- The constant term: [tex]\(-40\)[/tex]
4. Write the final simplified polynomial:
[tex]\[48x^3 - 4x^2 + 18x - 40\][/tex]
The answer is [tex]\[48x^3 - 4x^2 + 18x - 40\][/tex], which corresponds to option A.
1. Multiply each term in [tex]\((8x^2 + 6x + 8)\)[/tex] by [tex]\(6x\)[/tex]:
- [tex]\(8x^2 \times 6x = 48x^3\)[/tex]
- [tex]\(6x \times 6x = 36x^2\)[/tex]
- [tex]\(8 \times 6x = 48x\)[/tex]
2. Multiply each term in [tex]\((8x^2 + 6x + 8)\)[/tex] by [tex]\(-5\)[/tex]:
- [tex]\(8x^2 \times -5 = -40x^2\)[/tex]
- [tex]\(6x \times -5 = -30x\)[/tex]
- [tex]\(8 \times -5 = -40\)[/tex]
3. Combine all the results from steps 1 and 2:
- The [tex]\(x^3\)[/tex] term: [tex]\(48x^3\)[/tex]
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(36x^2 - 40x^2 = -4x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(48x - 30x = 18x\)[/tex]
- The constant term: [tex]\(-40\)[/tex]
4. Write the final simplified polynomial:
[tex]\[48x^3 - 4x^2 + 18x - 40\][/tex]
The answer is [tex]\[48x^3 - 4x^2 + 18x - 40\][/tex], which corresponds to option A.
