Answer :
To multiply the polynomials [tex]\((8x^2 + 6x + 8)\)[/tex] and [tex]\((6x - 5)\)[/tex], follow these steps:
1. Distribute each term of the first polynomial to each term of the second polynomial:
[tex]\[
(8x^2 + 6x + 8) \cdot (6x - 5) = 8x^2 \cdot (6x - 5) + 6x \cdot (6x - 5) + 8 \cdot (6x - 5)
\][/tex]
2. Multiply each pair of terms:
- 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]
- 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]
- Multiply [tex]\(8\)[/tex] by each term in [tex]\(6x - 5\)[/tex]:
[tex]\[
8 \cdot 6x = 48x
\][/tex]
[tex]\[
8 \cdot (-5) = -40
\][/tex]
3. Combine all the terms:
Add all the results from step 2:
[tex]\[
48x^3 + (-40x^2) + 36x^2 + (-30x) + 48x + (-40)
\][/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:
The resulting polynomial is:
[tex]\[
48x^3 - 4x^2 + 18x - 40
\][/tex]
So, the correct answer is A. [tex]\(48x^3 - 4x^2 + 18x - 40\)[/tex].
1. Distribute each term of the first polynomial to each term of the second polynomial:
[tex]\[
(8x^2 + 6x + 8) \cdot (6x - 5) = 8x^2 \cdot (6x - 5) + 6x \cdot (6x - 5) + 8 \cdot (6x - 5)
\][/tex]
2. Multiply each pair of terms:
- 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]
- 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]
- Multiply [tex]\(8\)[/tex] by each term in [tex]\(6x - 5\)[/tex]:
[tex]\[
8 \cdot 6x = 48x
\][/tex]
[tex]\[
8 \cdot (-5) = -40
\][/tex]
3. Combine all the terms:
Add all the results from step 2:
[tex]\[
48x^3 + (-40x^2) + 36x^2 + (-30x) + 48x + (-40)
\][/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:
The resulting polynomial is:
[tex]\[
48x^3 - 4x^2 + 18x - 40
\][/tex]
So, the correct answer is A. [tex]\(48x^3 - 4x^2 + 18x - 40\)[/tex].
