Answer :
To solve the problem of multiplying the polynomials [tex]\((8x^2 + 6x + 8)\)[/tex] and [tex]\((6x - 5)\)[/tex], we use the distributive property, which involves multiplying each term in the first polynomial by each term in the second polynomial and then combining like terms. Let's go through it step by step:
1. Identify the terms in each polynomial:
- The first polynomial is [tex]\(8x^2 + 6x + 8\)[/tex].
- The second polynomial is [tex]\(6x - 5\)[/tex].
2. Multiply each term in the first polynomial by each term in the second polynomial:
- Multiply [tex]\(8x^2\)[/tex] by both terms in [tex]\((6x - 5)\)[/tex]:
- [tex]\(8x^2 \cdot 6x = 48x^3\)[/tex]
- [tex]\(8x^2 \cdot (-5) = -40x^2\)[/tex]
- Multiply [tex]\(6x\)[/tex] by both terms in [tex]\((6x - 5)\)[/tex]:
- [tex]\(6x \cdot 6x = 36x^2\)[/tex]
- [tex]\(6x \cdot (-5) = -30x\)[/tex]
- Multiply [tex]\(8\)[/tex] by both terms in [tex]\((6x - 5)\)[/tex]:
- [tex]\(8 \cdot 6x = 48x\)[/tex]
- [tex]\(8 \cdot (-5) = -40\)[/tex]
3. Combine all the products:
- Write down all the products we obtained:
- [tex]\(48x^3\)[/tex]
- [tex]\(-40x^2\)[/tex]
- [tex]\(36x^2\)[/tex]
- [tex]\(-30x\)[/tex]
- [tex]\(48x\)[/tex]
- [tex]\(-40\)[/tex]
4. Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(-40x^2 + 36x^2 = -4x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-30x + 48x = 18x\)[/tex]
5. Write the final expression:
- [tex]\(48x^3 - 4x^2 + 18x - 40\)[/tex]
Therefore, the product of the polynomials [tex]\((8x^2 + 6x + 8)\)[/tex] and [tex]\((6x - 5)\)[/tex] is [tex]\(48x^3 - 4x^2 + 18x - 40\)[/tex].
The correct answer is: A. [tex]\(48x^3 - 4x^2 + 18x - 40\)[/tex].
1. Identify the terms in each polynomial:
- The first polynomial is [tex]\(8x^2 + 6x + 8\)[/tex].
- The second polynomial is [tex]\(6x - 5\)[/tex].
2. Multiply each term in the first polynomial by each term in the second polynomial:
- Multiply [tex]\(8x^2\)[/tex] by both terms in [tex]\((6x - 5)\)[/tex]:
- [tex]\(8x^2 \cdot 6x = 48x^3\)[/tex]
- [tex]\(8x^2 \cdot (-5) = -40x^2\)[/tex]
- Multiply [tex]\(6x\)[/tex] by both terms in [tex]\((6x - 5)\)[/tex]:
- [tex]\(6x \cdot 6x = 36x^2\)[/tex]
- [tex]\(6x \cdot (-5) = -30x\)[/tex]
- Multiply [tex]\(8\)[/tex] by both terms in [tex]\((6x - 5)\)[/tex]:
- [tex]\(8 \cdot 6x = 48x\)[/tex]
- [tex]\(8 \cdot (-5) = -40\)[/tex]
3. Combine all the products:
- Write down all the products we obtained:
- [tex]\(48x^3\)[/tex]
- [tex]\(-40x^2\)[/tex]
- [tex]\(36x^2\)[/tex]
- [tex]\(-30x\)[/tex]
- [tex]\(48x\)[/tex]
- [tex]\(-40\)[/tex]
4. Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(-40x^2 + 36x^2 = -4x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-30x + 48x = 18x\)[/tex]
5. Write the final expression:
- [tex]\(48x^3 - 4x^2 + 18x - 40\)[/tex]
Therefore, the product of the polynomials [tex]\((8x^2 + 6x + 8)\)[/tex] and [tex]\((6x - 5)\)[/tex] is [tex]\(48x^3 - 4x^2 + 18x - 40\)[/tex].
The correct answer is: A. [tex]\(48x^3 - 4x^2 + 18x - 40\)[/tex].
