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Answer :
Sure, let's solve the problem of multiplying the polynomials [tex]\((7x^2 + 9x + 7)(9x - 4)\)[/tex] step-by-step.
### Step 1: Distribute Each Term
To multiply the polynomials, we distribute each term in the first polynomial by each term in the second polynomial.
1. 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]
2. 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]
3. Multiply [tex]\(7\)[/tex] by each term in [tex]\(9x - 4\)[/tex]:
- [tex]\(7 \times 9x = 63x\)[/tex]
- [tex]\(7 \times -4 = -28\)[/tex]
### Step 2: Combine Like Terms
Now, combine all the results from the above multiplication:
- [tex]\(63x^3\)[/tex] (from [tex]\(7x^2 \times 9x\)[/tex])
- [tex]\(-28x^2 + 81x^2 = 53x^2\)[/tex] (combine the results from [tex]\(7x^2 \times -4\)[/tex] and [tex]\(9x \times 9x\)[/tex])
- [tex]\(-36x + 63x = 27x\)[/tex] (combine the results from [tex]\(9x \times -4\)[/tex] and [tex]\(7 \times 9x\)[/tex])
- [tex]\(-28\)[/tex] (from [tex]\(7 \times -4\)[/tex])
### Final Result:
Put all the terms together in order:
[tex]\[63x^3 + 53x^2 + 27x - 28\][/tex]
Therefore, the multiplied polynomial is [tex]\(63x^3 + 53x^2 + 27x - 28\)[/tex].
### Step 1: Distribute Each Term
To multiply the polynomials, we distribute each term in the first polynomial by each term in the second polynomial.
1. 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]
2. 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]
3. Multiply [tex]\(7\)[/tex] by each term in [tex]\(9x - 4\)[/tex]:
- [tex]\(7 \times 9x = 63x\)[/tex]
- [tex]\(7 \times -4 = -28\)[/tex]
### Step 2: Combine Like Terms
Now, combine all the results from the above multiplication:
- [tex]\(63x^3\)[/tex] (from [tex]\(7x^2 \times 9x\)[/tex])
- [tex]\(-28x^2 + 81x^2 = 53x^2\)[/tex] (combine the results from [tex]\(7x^2 \times -4\)[/tex] and [tex]\(9x \times 9x\)[/tex])
- [tex]\(-36x + 63x = 27x\)[/tex] (combine the results from [tex]\(9x \times -4\)[/tex] and [tex]\(7 \times 9x\)[/tex])
- [tex]\(-28\)[/tex] (from [tex]\(7 \times -4\)[/tex])
### Final Result:
Put all the terms together in order:
[tex]\[63x^3 + 53x^2 + 27x - 28\][/tex]
Therefore, the multiplied polynomial is [tex]\(63x^3 + 53x^2 + 27x - 28\)[/tex].
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