Answer :
To multiply the polynomials [tex]\((8x^2 + 6x + 8)(6x - 5)\)[/tex], we will use the distributive property, also known as the FOIL method for binomials.
1. Distribute each term in the first polynomial to each term in the second polynomial:
[tex]\[(8x^2 + 6x + 8)(6x - 5)\][/tex]
2. Let's start by distributing [tex]\(8x^2\)[/tex]:
[tex]\[8x^2 \cdot (6x - 5) = 48x^3 - 40x^2\][/tex]
3. Next, distribute [tex]\(6x\)[/tex]:
[tex]\[6x \cdot (6x - 5) = 36x^2 - 30x\][/tex]
4. Finally, distribute [tex]\(8\)[/tex]:
[tex]\[8 \cdot (6x - 5) = 48x - 40\][/tex]
5. Now, we combine all these distributed terms:
[tex]\[48x^3 - 40x^2 + 36x^2 - 30x + 48x - 40\][/tex]
6. 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]
So our expression becomes:
[tex]\[48x^3 - 4x^2 + 18x - 40\][/tex]
Therefore, the correct answer is:
C. [tex]\(48 x^3 - 4 x^2 + 18 x - 40\)[/tex]
1. Distribute each term in the first polynomial to each term in the second polynomial:
[tex]\[(8x^2 + 6x + 8)(6x - 5)\][/tex]
2. Let's start by distributing [tex]\(8x^2\)[/tex]:
[tex]\[8x^2 \cdot (6x - 5) = 48x^3 - 40x^2\][/tex]
3. Next, distribute [tex]\(6x\)[/tex]:
[tex]\[6x \cdot (6x - 5) = 36x^2 - 30x\][/tex]
4. Finally, distribute [tex]\(8\)[/tex]:
[tex]\[8 \cdot (6x - 5) = 48x - 40\][/tex]
5. Now, we combine all these distributed terms:
[tex]\[48x^3 - 40x^2 + 36x^2 - 30x + 48x - 40\][/tex]
6. 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]
So our expression becomes:
[tex]\[48x^3 - 4x^2 + 18x - 40\][/tex]
Therefore, the correct answer is:
C. [tex]\(48 x^3 - 4 x^2 + 18 x - 40\)[/tex]
