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Answer :
To multiply the polynomials [tex]\((7x^2 + 9x + 7)(9x - 4)\)[/tex], we'll distribute each term in the first polynomial by each term in the second polynomial and then combine like terms. Here's a step-by-step solution:
1. Multiply each term in the first polynomial by each term in the second polynomial:
- Multiply [tex]\(7x^2\)[/tex] by [tex]\(9x\)[/tex]:
[tex]\[7x^2 \times 9x = 63x^3\][/tex]
- Multiply [tex]\(7x^2\)[/tex] by [tex]\(-4\)[/tex]:
[tex]\[7x^2 \times -4 = -28x^2\][/tex]
- Multiply [tex]\(9x\)[/tex] by [tex]\(9x\)[/tex]:
[tex]\[9x \times 9x = 81x^2\][/tex]
- Multiply [tex]\(9x\)[/tex] by [tex]\(-4\)[/tex]:
[tex]\[9x \times -4 = -36x\][/tex]
- Multiply [tex]\(7\)[/tex] by [tex]\(9x\)[/tex]:
[tex]\[7 \times 9x = 63x\][/tex]
- Multiply [tex]\(7\)[/tex] by [tex]\(-4\)[/tex]:
[tex]\[7 \times -4 = -28\][/tex]
2. Combine all these results:
- [tex]\(63x^3\)[/tex]
- [tex]\((-28x^2 + 81x^2)\)[/tex] gives [tex]\((81x^2 - 28x^2) = 53x^2\)[/tex]
- [tex]\((-36x + 63x)\)[/tex] gives [tex]\((63x - 36x) = 27x\)[/tex]
- [tex]\(-28\)[/tex]
3. Write the final expression by combining all the terms:
[tex]\[63x^3 + 53x^2 + 27x - 28\][/tex]
So, the correct multiplication result is:
[tex]\[63x^3 + 53x^2 + 27x - 28\][/tex]
The correct answer is option D: [tex]\(63x^3 + 53x^2 + 27x - 28\)[/tex].
1. Multiply each term in the first polynomial by each term in the second polynomial:
- Multiply [tex]\(7x^2\)[/tex] by [tex]\(9x\)[/tex]:
[tex]\[7x^2 \times 9x = 63x^3\][/tex]
- Multiply [tex]\(7x^2\)[/tex] by [tex]\(-4\)[/tex]:
[tex]\[7x^2 \times -4 = -28x^2\][/tex]
- Multiply [tex]\(9x\)[/tex] by [tex]\(9x\)[/tex]:
[tex]\[9x \times 9x = 81x^2\][/tex]
- Multiply [tex]\(9x\)[/tex] by [tex]\(-4\)[/tex]:
[tex]\[9x \times -4 = -36x\][/tex]
- Multiply [tex]\(7\)[/tex] by [tex]\(9x\)[/tex]:
[tex]\[7 \times 9x = 63x\][/tex]
- Multiply [tex]\(7\)[/tex] by [tex]\(-4\)[/tex]:
[tex]\[7 \times -4 = -28\][/tex]
2. Combine all these results:
- [tex]\(63x^3\)[/tex]
- [tex]\((-28x^2 + 81x^2)\)[/tex] gives [tex]\((81x^2 - 28x^2) = 53x^2\)[/tex]
- [tex]\((-36x + 63x)\)[/tex] gives [tex]\((63x - 36x) = 27x\)[/tex]
- [tex]\(-28\)[/tex]
3. Write the final expression by combining all the terms:
[tex]\[63x^3 + 53x^2 + 27x - 28\][/tex]
So, the correct multiplication result is:
[tex]\[63x^3 + 53x^2 + 27x - 28\][/tex]
The correct answer is option D: [tex]\(63x^3 + 53x^2 + 27x - 28\)[/tex].
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