Answer :
To multiply the polynomials [tex]\((8x^2 + 6x + 8)\)[/tex] and [tex]\((6x - 5)\)[/tex], we'll use the distributive property, which involves multiplying each term in the first polynomial by each term in the second polynomial. Let's go through this step-by-step:
1. Multiply [tex]\(8x^2\)[/tex] by each term in [tex]\((6x - 5)\)[/tex]:
- [tex]\(8x^2 \cdot 6x = 48x^3\)[/tex]
- [tex]\(8x^2 \cdot -5 = -40x^2\)[/tex]
2. Multiply [tex]\(6x\)[/tex] by each term in [tex]\((6x - 5)\)[/tex]:
- [tex]\(6x \cdot 6x = 36x^2\)[/tex]
- [tex]\(6x \cdot -5 = -30x\)[/tex]
3. Multiply [tex]\(8\)[/tex] by each term in [tex]\((6x - 5)\)[/tex]:
- [tex]\(8 \cdot 6x = 48x\)[/tex]
- [tex]\(8 \cdot -5 = -40\)[/tex]
4. Combine the like terms:
- The [tex]\(x^3\)[/tex] term: [tex]\(48x^3\)[/tex]
- The [tex]\(x^2\)[/tex] terms: [tex]\(-40x^2 + 36x^2 = -4x^2\)[/tex]
- The [tex]\(x\)[/tex] terms: [tex]\(-30x + 48x = 18x\)[/tex]
- The constant term: [tex]\(-40\)[/tex]
So, the final result of multiplying the polynomials is:
[tex]\[48x^3 - 4x^2 + 18x - 40\][/tex]
This corresponds to option C in the given choices.
1. Multiply [tex]\(8x^2\)[/tex] by each term in [tex]\((6x - 5)\)[/tex]:
- [tex]\(8x^2 \cdot 6x = 48x^3\)[/tex]
- [tex]\(8x^2 \cdot -5 = -40x^2\)[/tex]
2. Multiply [tex]\(6x\)[/tex] by each term in [tex]\((6x - 5)\)[/tex]:
- [tex]\(6x \cdot 6x = 36x^2\)[/tex]
- [tex]\(6x \cdot -5 = -30x\)[/tex]
3. Multiply [tex]\(8\)[/tex] by each term in [tex]\((6x - 5)\)[/tex]:
- [tex]\(8 \cdot 6x = 48x\)[/tex]
- [tex]\(8 \cdot -5 = -40\)[/tex]
4. Combine the like terms:
- The [tex]\(x^3\)[/tex] term: [tex]\(48x^3\)[/tex]
- The [tex]\(x^2\)[/tex] terms: [tex]\(-40x^2 + 36x^2 = -4x^2\)[/tex]
- The [tex]\(x\)[/tex] terms: [tex]\(-30x + 48x = 18x\)[/tex]
- The constant term: [tex]\(-40\)[/tex]
So, the final result of multiplying the polynomials is:
[tex]\[48x^3 - 4x^2 + 18x - 40\][/tex]
This corresponds to option C in the given choices.
