Answer :
Sure! Let's multiply the polynomials [tex]\((7x^2 + 5x + 7)\)[/tex] and [tex]\((4x - 6)\)[/tex] step by step:
1. Distribute each term in [tex]\((4x - 6)\)[/tex] to each term in [tex]\((7x^2 + 5x + 7)\)[/tex]:
- Multiply [tex]\(4x\)[/tex] by each term in [tex]\((7x^2 + 5x + 7)\)[/tex]:
- [tex]\(4x \cdot 7x^2 = 28x^3\)[/tex]
- [tex]\(4x \cdot 5x = 20x^2\)[/tex]
- [tex]\(4x \cdot 7 = 28x\)[/tex]
- Multiply [tex]\(-6\)[/tex] by each term in [tex]\((7x^2 + 5x + 7)\)[/tex]:
- [tex]\(-6 \cdot 7x^2 = -42x^2\)[/tex]
- [tex]\(-6 \cdot 5x = -30x\)[/tex]
- [tex]\(-6 \cdot 7 = -42\)[/tex]
2. Combine all these results together:
[tex]\[
28x^3 + 20x^2 + 28x - 42x^2 - 30x - 42
\][/tex]
3. Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(20x^2 - 42x^2 = -22x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(28x - 30x = -2x\)[/tex]
4. Write the final polynomial:
[tex]\[
28x^3 - 22x^2 - 2x - 42
\][/tex]
So, the final answer is:
D. [tex]\(28x^3 - 22x^2 - 2x - 42\)[/tex]
1. Distribute each term in [tex]\((4x - 6)\)[/tex] to each term in [tex]\((7x^2 + 5x + 7)\)[/tex]:
- Multiply [tex]\(4x\)[/tex] by each term in [tex]\((7x^2 + 5x + 7)\)[/tex]:
- [tex]\(4x \cdot 7x^2 = 28x^3\)[/tex]
- [tex]\(4x \cdot 5x = 20x^2\)[/tex]
- [tex]\(4x \cdot 7 = 28x\)[/tex]
- Multiply [tex]\(-6\)[/tex] by each term in [tex]\((7x^2 + 5x + 7)\)[/tex]:
- [tex]\(-6 \cdot 7x^2 = -42x^2\)[/tex]
- [tex]\(-6 \cdot 5x = -30x\)[/tex]
- [tex]\(-6 \cdot 7 = -42\)[/tex]
2. Combine all these results together:
[tex]\[
28x^3 + 20x^2 + 28x - 42x^2 - 30x - 42
\][/tex]
3. Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(20x^2 - 42x^2 = -22x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(28x - 30x = -2x\)[/tex]
4. Write the final polynomial:
[tex]\[
28x^3 - 22x^2 - 2x - 42
\][/tex]
So, the final answer is:
D. [tex]\(28x^3 - 22x^2 - 2x - 42\)[/tex]
