Answer :
Sure! Let's multiply the polynomials [tex]\((5x^2 + 2x + 8)\)[/tex] and [tex]\((7x - 6)\)[/tex] step-by-step:
1. Distribute each term in the first polynomial to each term in the second polynomial:
- 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]
- 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]
- Multiply [tex]\(8\)[/tex] by each term in [tex]\((7x - 6)\)[/tex]:
- [tex]\(8 \cdot 7x = 56x\)[/tex]
- [tex]\(8 \cdot (-6) = -48\)[/tex]
2. Combine all these terms together:
[tex]\[35x^3 + (-30x^2) + 14x^2 + (-12x) + 56x - 48\][/tex]
3. Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(-30x^2 + 14x^2 = -16x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-12x + 56x = 44x\)[/tex]
4. Write the final expression:
[tex]\[35x^3 - 16x^2 + 44x - 48\][/tex]
So, the correct answer is:
[tex]\[
\boxed{35x^3 - 16x^2 + 44x - 48}
\][/tex]
This matches option A.
1. Distribute each term in the first polynomial to each term in the second polynomial:
- 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]
- 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]
- Multiply [tex]\(8\)[/tex] by each term in [tex]\((7x - 6)\)[/tex]:
- [tex]\(8 \cdot 7x = 56x\)[/tex]
- [tex]\(8 \cdot (-6) = -48\)[/tex]
2. Combine all these terms together:
[tex]\[35x^3 + (-30x^2) + 14x^2 + (-12x) + 56x - 48\][/tex]
3. Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(-30x^2 + 14x^2 = -16x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-12x + 56x = 44x\)[/tex]
4. Write the final expression:
[tex]\[35x^3 - 16x^2 + 44x - 48\][/tex]
So, the correct answer is:
[tex]\[
\boxed{35x^3 - 16x^2 + 44x - 48}
\][/tex]
This matches option A.
