Answer :
Sure, let's multiply the given polynomials [tex]\((7x^2 + 9x + 7)\)[/tex] and [tex]\((9x - 4)\)[/tex] step-by-step.
1. Distribute each term in the first polynomial by each term in the second polynomial.
- Multiply [tex]\(7x^2\)[/tex] by each term in [tex]\((9x - 4)\)[/tex]:
- [tex]\(7x^2 \times 9x = 63x^3\)[/tex]
- [tex]\(7x^2 \times (-4) = -28x^2\)[/tex]
- Multiply [tex]\(9x\)[/tex] by each term in [tex]\((9x - 4)\)[/tex]:
- [tex]\(9x \times 9x = 81x^2\)[/tex]
- [tex]\(9x \times (-4) = -36x\)[/tex]
- Multiply [tex]\(7\)[/tex] by each term in [tex]\((9x - 4)\)[/tex]:
- [tex]\(7 \times 9x = 63x\)[/tex]
- [tex]\(7 \times (-4) = -28\)[/tex]
2. Combine all the like terms.
- For [tex]\(x^3\)[/tex] terms, there’s only one term: [tex]\(63x^3\)[/tex].
- For [tex]\(x^2\)[/tex] terms, combine [tex]\(-28x^2\)[/tex] and [tex]\(81x^2\)[/tex] to get:
[tex]\(-28x^2 + 81x^2 = 53x^2\)[/tex].
- For [tex]\(x\)[/tex] terms, combine [tex]\(-36x\)[/tex] and [tex]\(63x\)[/tex] to get:
[tex]\(-36x + 63x = 27x\)[/tex].
- The constant term is [tex]\(-28\)[/tex].
3. Write the final expression by combining these results.
So, the polynomial resulting from the multiplication is:
[tex]\[63x^3 + 53x^2 + 27x - 28\][/tex]
Therefore, the correct answer is [tex]\( \boxed{B. \, 63x^3 + 53x^2 + 27x - 28} \)[/tex].
1. Distribute each term in the first polynomial by each term in the second polynomial.
- Multiply [tex]\(7x^2\)[/tex] by each term in [tex]\((9x - 4)\)[/tex]:
- [tex]\(7x^2 \times 9x = 63x^3\)[/tex]
- [tex]\(7x^2 \times (-4) = -28x^2\)[/tex]
- Multiply [tex]\(9x\)[/tex] by each term in [tex]\((9x - 4)\)[/tex]:
- [tex]\(9x \times 9x = 81x^2\)[/tex]
- [tex]\(9x \times (-4) = -36x\)[/tex]
- Multiply [tex]\(7\)[/tex] by each term in [tex]\((9x - 4)\)[/tex]:
- [tex]\(7 \times 9x = 63x\)[/tex]
- [tex]\(7 \times (-4) = -28\)[/tex]
2. Combine all the like terms.
- For [tex]\(x^3\)[/tex] terms, there’s only one term: [tex]\(63x^3\)[/tex].
- For [tex]\(x^2\)[/tex] terms, combine [tex]\(-28x^2\)[/tex] and [tex]\(81x^2\)[/tex] to get:
[tex]\(-28x^2 + 81x^2 = 53x^2\)[/tex].
- For [tex]\(x\)[/tex] terms, combine [tex]\(-36x\)[/tex] and [tex]\(63x\)[/tex] to get:
[tex]\(-36x + 63x = 27x\)[/tex].
- The constant term is [tex]\(-28\)[/tex].
3. Write the final expression by combining these results.
So, the polynomial resulting from the multiplication is:
[tex]\[63x^3 + 53x^2 + 27x - 28\][/tex]
Therefore, the correct answer is [tex]\( \boxed{B. \, 63x^3 + 53x^2 + 27x - 28} \)[/tex].
