Answer :
Let's multiply the polynomials [tex]\((8x^2 + 6x + 8)\)[/tex] and [tex]\((6x - 5)\)[/tex] using the distributive property (also known as the FOIL method for multiplying polynomials more than a binomial).
1. First, distribute the [tex]\(6x\)[/tex] term:
- [tex]\(8x^2 \times 6x = 48x^3\)[/tex]
- [tex]\(6x \times 6x = 36x^2\)[/tex]
- [tex]\(8 \times 6x = 48x\)[/tex]
So, multiplying by [tex]\(6x\)[/tex] gives: [tex]\(48x^3 + 36x^2 + 48x\)[/tex].
2. Next, distribute the [tex]\(-5\)[/tex] term:
- [tex]\(8x^2 \times -5 = -40x^2\)[/tex]
- [tex]\(6x \times -5 = -30x\)[/tex]
- [tex]\(8 \times -5 = -40\)[/tex]
So, multiplying by [tex]\(-5\)[/tex] gives: [tex]\(-40x^2 - 30x - 40\)[/tex].
3. Now, combine all the results:
- [tex]\(48x^3 + 36x^2 + 48x\)[/tex]
- [tex]\(+ \, (-40x^2 - 30x - 40)\)[/tex]
4. Combine like terms:
- [tex]\(48x^3\)[/tex] remains as it is.
- [tex]\(36x^2 - 40x^2 = -4x^2\)[/tex]
- [tex]\(48x - 30x = 18x\)[/tex]
- [tex]\(-40\)[/tex] remains as it is.
So, the final result is:
[tex]\[48x^3 - 4x^2 + 18x - 40\][/tex]
Hence, the correct answer is B. [tex]\(48x^3 - 4x^2 + 18x - 40\)[/tex].
1. First, distribute the [tex]\(6x\)[/tex] term:
- [tex]\(8x^2 \times 6x = 48x^3\)[/tex]
- [tex]\(6x \times 6x = 36x^2\)[/tex]
- [tex]\(8 \times 6x = 48x\)[/tex]
So, multiplying by [tex]\(6x\)[/tex] gives: [tex]\(48x^3 + 36x^2 + 48x\)[/tex].
2. Next, distribute the [tex]\(-5\)[/tex] term:
- [tex]\(8x^2 \times -5 = -40x^2\)[/tex]
- [tex]\(6x \times -5 = -30x\)[/tex]
- [tex]\(8 \times -5 = -40\)[/tex]
So, multiplying by [tex]\(-5\)[/tex] gives: [tex]\(-40x^2 - 30x - 40\)[/tex].
3. Now, combine all the results:
- [tex]\(48x^3 + 36x^2 + 48x\)[/tex]
- [tex]\(+ \, (-40x^2 - 30x - 40)\)[/tex]
4. Combine like terms:
- [tex]\(48x^3\)[/tex] remains as it is.
- [tex]\(36x^2 - 40x^2 = -4x^2\)[/tex]
- [tex]\(48x - 30x = 18x\)[/tex]
- [tex]\(-40\)[/tex] remains as it is.
So, the final result is:
[tex]\[48x^3 - 4x^2 + 18x - 40\][/tex]
Hence, the correct answer is B. [tex]\(48x^3 - 4x^2 + 18x - 40\)[/tex].
