Answer :
Sure! Let's multiply the polynomials [tex]\((5x^2 + 2x + 8)\)[/tex] and [tex]\((7x - 6)\)[/tex] step by step.
1. Distribute: We will distribute each term in the first polynomial [tex]\((5x^2 + 2x + 8)\)[/tex] by each term in the second polynomial [tex]\((7x - 6)\)[/tex].
2. Multiply [tex]\(5x^2\)[/tex] by each term in [tex]\((7x - 6)\)[/tex]:
- [tex]\(5x^2 \cdot 7x = 35x^3\)[/tex]
- [tex]\(5x^2 \cdot (-6) = -30x^2\)[/tex]
3. Multiply [tex]\(2x\)[/tex] by each term in [tex]\((7x - 6)\)[/tex]:
- [tex]\(2x \cdot 7x = 14x^2\)[/tex]
- [tex]\(2x \cdot (-6) = -12x\)[/tex]
4. Multiply [tex]\(8\)[/tex] by each term in [tex]\((7x - 6)\)[/tex]:
- [tex]\(8 \cdot 7x = 56x\)[/tex]
- [tex]\(8 \cdot (-6) = -48\)[/tex]
5. Combine all the terms:
- Combine like terms from the distributed results:
- [tex]\(35x^3\)[/tex] (no like terms)
- [tex]\((-30x^2 + 14x^2 = -16x^2)\)[/tex]
- [tex]\((-12x + 56x = 44x)\)[/tex]
- [tex]\(-48\)[/tex] (no like terms)
6. Final result:
[tex]\[
35x^3 - 16x^2 + 44x - 48
\][/tex]
So, the correct answer is D. [tex]\(35x^3 - 16x^2 + 44x - 48\)[/tex].
1. Distribute: We will distribute each term in the first polynomial [tex]\((5x^2 + 2x + 8)\)[/tex] by each term in the second polynomial [tex]\((7x - 6)\)[/tex].
2. Multiply [tex]\(5x^2\)[/tex] by each term in [tex]\((7x - 6)\)[/tex]:
- [tex]\(5x^2 \cdot 7x = 35x^3\)[/tex]
- [tex]\(5x^2 \cdot (-6) = -30x^2\)[/tex]
3. Multiply [tex]\(2x\)[/tex] by each term in [tex]\((7x - 6)\)[/tex]:
- [tex]\(2x \cdot 7x = 14x^2\)[/tex]
- [tex]\(2x \cdot (-6) = -12x\)[/tex]
4. Multiply [tex]\(8\)[/tex] by each term in [tex]\((7x - 6)\)[/tex]:
- [tex]\(8 \cdot 7x = 56x\)[/tex]
- [tex]\(8 \cdot (-6) = -48\)[/tex]
5. Combine all the terms:
- Combine like terms from the distributed results:
- [tex]\(35x^3\)[/tex] (no like terms)
- [tex]\((-30x^2 + 14x^2 = -16x^2)\)[/tex]
- [tex]\((-12x + 56x = 44x)\)[/tex]
- [tex]\(-48\)[/tex] (no like terms)
6. Final result:
[tex]\[
35x^3 - 16x^2 + 44x - 48
\][/tex]
So, the correct answer is D. [tex]\(35x^3 - 16x^2 + 44x - 48\)[/tex].
