Answer :
To multiply the polynomials [tex]\((8x^2 + 6x + 8)(6x - 5)\)[/tex], we will use distributive property, also known as the FOIL method for binomials, applied here for a trinomial and a binomial.
Let's multiply each term in the first polynomial by each term in the second polynomial:
1. Multiply [tex]\(8x^2\)[/tex] by each term in [tex]\((6x - 5)\)[/tex]:
- [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 [tex]\((6x - 5)\)[/tex]:
- [tex]\(6x \times 6x = 36x^2\)[/tex]
- [tex]\(6x \times -5 = -30x\)[/tex]
3. Multiply [tex]\(8\)[/tex] by each term in [tex]\((6x - 5)\)[/tex]:
- [tex]\(8 \times 6x = 48x\)[/tex]
- [tex]\(8 \times -5 = -40\)[/tex]
Next, let's combine all these products:
- [tex]\(48x^3\)[/tex] from the first step.
- Add the results for [tex]\(x^2\)[/tex] terms: [tex]\(-40x^2 + 36x^2 = -4x^2\)[/tex]
- Add the results for [tex]\(x\)[/tex] terms: [tex]\(-30x + 48x = 18x\)[/tex]
- The constant term is [tex]\(-40\)[/tex].
Putting it all together, the product of the polynomials is:
[tex]\[ 48x^3 - 4x^2 + 18x - 40 \][/tex]
Therefore, the correct answer is: [tex]\(48x^3 - 4x^2 + 18x - 40\)[/tex].
Let's multiply each term in the first polynomial by each term in the second polynomial:
1. Multiply [tex]\(8x^2\)[/tex] by each term in [tex]\((6x - 5)\)[/tex]:
- [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 [tex]\((6x - 5)\)[/tex]:
- [tex]\(6x \times 6x = 36x^2\)[/tex]
- [tex]\(6x \times -5 = -30x\)[/tex]
3. Multiply [tex]\(8\)[/tex] by each term in [tex]\((6x - 5)\)[/tex]:
- [tex]\(8 \times 6x = 48x\)[/tex]
- [tex]\(8 \times -5 = -40\)[/tex]
Next, let's combine all these products:
- [tex]\(48x^3\)[/tex] from the first step.
- Add the results for [tex]\(x^2\)[/tex] terms: [tex]\(-40x^2 + 36x^2 = -4x^2\)[/tex]
- Add the results for [tex]\(x\)[/tex] terms: [tex]\(-30x + 48x = 18x\)[/tex]
- The constant term is [tex]\(-40\)[/tex].
Putting it all together, the product of the polynomials is:
[tex]\[ 48x^3 - 4x^2 + 18x - 40 \][/tex]
Therefore, the correct answer is: [tex]\(48x^3 - 4x^2 + 18x - 40\)[/tex].
