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Answer :
To multiply the polynomials [tex]\((8x^2 + 6x + 8)\)[/tex] and [tex]\((6x - 5)\)[/tex], we'll use the distributive property. This means we'll multiply each term in the first polynomial by each term in the second polynomial and then combine like terms.
1. Multiply each term of [tex]\((6x - 5)\)[/tex] by [tex]\(8x^2\)[/tex]:
- [tex]\(8x^2 \cdot 6x = 48x^3\)[/tex]
- [tex]\(8x^2 \cdot (-5) = -40x^2\)[/tex]
2. Multiply each term of [tex]\((6x - 5)\)[/tex] by [tex]\(6x\)[/tex]:
- [tex]\(6x \cdot 6x = 36x^2\)[/tex]
- [tex]\(6x \cdot (-5) = -30x\)[/tex]
3. Multiply each term of [tex]\((6x - 5)\)[/tex] by [tex]\(8\)[/tex]:
- [tex]\(8 \cdot 6x = 48x\)[/tex]
- [tex]\(8 \cdot (-5) = -40\)[/tex]
Now, we add all these results together:
[tex]\[ 48x^3 + (-40x^2) + 36x^2 + (-30x) + 48x + (-40) \][/tex]
Combine the like terms:
- The cubic term: [tex]\(48x^3\)[/tex]
- The quadratic terms: [tex]\(-40x^2 + 36x^2 = -4x^2\)[/tex]
- The linear terms: [tex]\(-30x + 48x = 18x\)[/tex]
- The constant term: [tex]\(-40\)[/tex]
Thus, the resulting polynomial is:
[tex]\[ 48x^3 - 4x^2 + 18x - 40 \][/tex]
So, the correct choice is B. [tex]\(48x^3 - 4x^2 + 18x - 40\)[/tex].
1. Multiply each term of [tex]\((6x - 5)\)[/tex] by [tex]\(8x^2\)[/tex]:
- [tex]\(8x^2 \cdot 6x = 48x^3\)[/tex]
- [tex]\(8x^2 \cdot (-5) = -40x^2\)[/tex]
2. Multiply each term of [tex]\((6x - 5)\)[/tex] by [tex]\(6x\)[/tex]:
- [tex]\(6x \cdot 6x = 36x^2\)[/tex]
- [tex]\(6x \cdot (-5) = -30x\)[/tex]
3. Multiply each term of [tex]\((6x - 5)\)[/tex] by [tex]\(8\)[/tex]:
- [tex]\(8 \cdot 6x = 48x\)[/tex]
- [tex]\(8 \cdot (-5) = -40\)[/tex]
Now, we add all these results together:
[tex]\[ 48x^3 + (-40x^2) + 36x^2 + (-30x) + 48x + (-40) \][/tex]
Combine the like terms:
- The cubic term: [tex]\(48x^3\)[/tex]
- The quadratic terms: [tex]\(-40x^2 + 36x^2 = -4x^2\)[/tex]
- The linear terms: [tex]\(-30x + 48x = 18x\)[/tex]
- The constant term: [tex]\(-40\)[/tex]
Thus, the resulting polynomial is:
[tex]\[ 48x^3 - 4x^2 + 18x - 40 \][/tex]
So, the correct choice is B. [tex]\(48x^3 - 4x^2 + 18x - 40\)[/tex].
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