Answer :
To multiply the polynomials [tex]\((7x^2 + 9x + 7)(9x - 4)\)[/tex], we'll use the distributive property (also known as the FOIL method for binomials), applying it to each term in one polynomial to each term in the other polynomial.
1. Distribute [tex]\(7x^2\)[/tex] in [tex]\((7x^2 + 9x + 7)\)[/tex] to each term in [tex]\((9x - 4)\)[/tex]:
- [tex]\(7x^2 \times 9x = 63x^3\)[/tex]
- [tex]\(7x^2 \times -4 = -28x^2\)[/tex]
2. Distribute [tex]\(9x\)[/tex] in [tex]\((7x^2 + 9x + 7)\)[/tex] to each term in [tex]\((9x - 4)\)[/tex]:
- [tex]\(9x \times 9x = 81x^2\)[/tex]
- [tex]\(9x \times -4 = -36x\)[/tex]
3. Distribute [tex]\(7\)[/tex] in [tex]\((7x^2 + 9x + 7)\)[/tex] to each term in [tex]\((9x - 4)\)[/tex]:
- [tex]\(7 \times 9x = 63x\)[/tex]
- [tex]\(7 \times -4 = -28\)[/tex]
4. Combine all the terms:
- Collect the [tex]\(x^3\)[/tex] terms: [tex]\(63x^3\)[/tex]
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(-28x^2 + 81x^2 = 53x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-36x + 63x = 27x\)[/tex]
- The constant term: [tex]\(-28\)[/tex]
Putting it all together, the result of [tex]\((7x^2 + 9x + 7)(9x - 4)\)[/tex] is:
[tex]\[
63x^3 + 53x^2 + 27x - 28
\][/tex]
Therefore, the correct choice is:
D. [tex]\(63x^3 + 53x^2 + 27x - 28\)[/tex]
1. Distribute [tex]\(7x^2\)[/tex] in [tex]\((7x^2 + 9x + 7)\)[/tex] to each term in [tex]\((9x - 4)\)[/tex]:
- [tex]\(7x^2 \times 9x = 63x^3\)[/tex]
- [tex]\(7x^2 \times -4 = -28x^2\)[/tex]
2. Distribute [tex]\(9x\)[/tex] in [tex]\((7x^2 + 9x + 7)\)[/tex] to each term in [tex]\((9x - 4)\)[/tex]:
- [tex]\(9x \times 9x = 81x^2\)[/tex]
- [tex]\(9x \times -4 = -36x\)[/tex]
3. Distribute [tex]\(7\)[/tex] in [tex]\((7x^2 + 9x + 7)\)[/tex] to each term in [tex]\((9x - 4)\)[/tex]:
- [tex]\(7 \times 9x = 63x\)[/tex]
- [tex]\(7 \times -4 = -28\)[/tex]
4. Combine all the terms:
- Collect the [tex]\(x^3\)[/tex] terms: [tex]\(63x^3\)[/tex]
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(-28x^2 + 81x^2 = 53x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-36x + 63x = 27x\)[/tex]
- The constant term: [tex]\(-28\)[/tex]
Putting it all together, the result of [tex]\((7x^2 + 9x + 7)(9x - 4)\)[/tex] is:
[tex]\[
63x^3 + 53x^2 + 27x - 28
\][/tex]
Therefore, the correct choice is:
D. [tex]\(63x^3 + 53x^2 + 27x - 28\)[/tex]
