Answer :
To multiply the polynomials [tex]\((8x^2 + 6x + 8)(6x - 5)\)[/tex], we will use the distributive property to multiply each term in the first polynomial by each term in the second polynomial. Here are the steps:
1. Multiply [tex]\(8x^2\)[/tex] by each term in the second polynomial:
- [tex]\(8x^2 \times 6x = 48x^3\)[/tex]
- [tex]\(8x^2 \times -5 = -40x^2\)[/tex]
2. Multiply [tex]\(6x\)[/tex] by each term in the second polynomial:
- [tex]\(6x \times 6x = 36x^2\)[/tex]
- [tex]\(6x \times -5 = -30x\)[/tex]
3. Multiply [tex]\(8\)[/tex] by each term in the second polynomial:
- [tex]\(8 \times 6x = 48x\)[/tex]
- [tex]\(8 \times -5 = -40\)[/tex]
4. Combine all these results:
- [tex]\(48x^3\)[/tex] (from step 1)
- [tex]\(-40x^2 + 36x^2 = -4x^2\)[/tex] (combine like terms from steps 1 and 2)
- [tex]\(-30x + 48x = 18x\)[/tex] (combine like terms from steps 2 and 3)
- [tex]\(-40\)[/tex] (from step 3)
5. Write the final polynomial expression:
The result is [tex]\(48x^3 - 4x^2 + 18x - 40\)[/tex].
This matches option A: [tex]\(48x^3 - 4x^2 + 18x - 40\)[/tex].
1. Multiply [tex]\(8x^2\)[/tex] by each term in the second polynomial:
- [tex]\(8x^2 \times 6x = 48x^3\)[/tex]
- [tex]\(8x^2 \times -5 = -40x^2\)[/tex]
2. Multiply [tex]\(6x\)[/tex] by each term in the second polynomial:
- [tex]\(6x \times 6x = 36x^2\)[/tex]
- [tex]\(6x \times -5 = -30x\)[/tex]
3. Multiply [tex]\(8\)[/tex] by each term in the second polynomial:
- [tex]\(8 \times 6x = 48x\)[/tex]
- [tex]\(8 \times -5 = -40\)[/tex]
4. Combine all these results:
- [tex]\(48x^3\)[/tex] (from step 1)
- [tex]\(-40x^2 + 36x^2 = -4x^2\)[/tex] (combine like terms from steps 1 and 2)
- [tex]\(-30x + 48x = 18x\)[/tex] (combine like terms from steps 2 and 3)
- [tex]\(-40\)[/tex] (from step 3)
5. Write the final polynomial expression:
The result is [tex]\(48x^3 - 4x^2 + 18x - 40\)[/tex].
This matches option A: [tex]\(48x^3 - 4x^2 + 18x - 40\)[/tex].
