Answer :
To solve the problem of multiplying the polynomials [tex]\((7x^2 + 9x + 7)(9x - 4)\)[/tex], follow these steps:
1. Distribute each term in the first polynomial across each term in the second polynomial.
- Step 1: Multiply the first term in [tex]\((7x^2 + 9x + 7)\)[/tex] by each term in [tex]\((9x - 4)\)[/tex]:
- [tex]\(7x^2 \cdot 9x = 63x^3\)[/tex]
- [tex]\(7x^2 \cdot (-4) = -28x^2\)[/tex]
- Step 2: Multiply the second term in [tex]\((7x^2 + 9x + 7)\)[/tex] by each term in [tex]\((9x - 4)\)[/tex]:
- [tex]\(9x \cdot 9x = 81x^2\)[/tex]
- [tex]\(9x \cdot (-4) = -36x\)[/tex]
- Step 3: Multiply the third term in [tex]\((7x^2 + 9x + 7)\)[/tex] by each term in [tex]\((9x - 4)\)[/tex]:
- [tex]\(7 \cdot 9x = 63x\)[/tex]
- [tex]\(7 \cdot (-4) = -28\)[/tex]
2. Add all the resulting terms together:
- From the calculations, we have:
- [tex]\(63x^3\)[/tex]
- [tex]\(-28x^2 + 81x^2 = 53x^2\)[/tex]
- [tex]\(-36x + 63x = 27x\)[/tex]
- [tex]\(-28\)[/tex]
3. Combine like terms:
- The terms are already expanded and combined: [tex]\(63x^3 + 53x^2 + 27x - 28\)[/tex].
Based on these calculations, the correct answer is A: [tex]\(63x^3 + 53x^2 + 27x - 28\)[/tex].
1. Distribute each term in the first polynomial across each term in the second polynomial.
- Step 1: Multiply the first term in [tex]\((7x^2 + 9x + 7)\)[/tex] by each term in [tex]\((9x - 4)\)[/tex]:
- [tex]\(7x^2 \cdot 9x = 63x^3\)[/tex]
- [tex]\(7x^2 \cdot (-4) = -28x^2\)[/tex]
- Step 2: Multiply the second term in [tex]\((7x^2 + 9x + 7)\)[/tex] by each term in [tex]\((9x - 4)\)[/tex]:
- [tex]\(9x \cdot 9x = 81x^2\)[/tex]
- [tex]\(9x \cdot (-4) = -36x\)[/tex]
- Step 3: Multiply the third term in [tex]\((7x^2 + 9x + 7)\)[/tex] by each term in [tex]\((9x - 4)\)[/tex]:
- [tex]\(7 \cdot 9x = 63x\)[/tex]
- [tex]\(7 \cdot (-4) = -28\)[/tex]
2. Add all the resulting terms together:
- From the calculations, we have:
- [tex]\(63x^3\)[/tex]
- [tex]\(-28x^2 + 81x^2 = 53x^2\)[/tex]
- [tex]\(-36x + 63x = 27x\)[/tex]
- [tex]\(-28\)[/tex]
3. Combine like terms:
- The terms are already expanded and combined: [tex]\(63x^3 + 53x^2 + 27x - 28\)[/tex].
Based on these calculations, the correct answer is A: [tex]\(63x^3 + 53x^2 + 27x - 28\)[/tex].
