Answer :
Sure! Let's multiply the polynomials step by step:
We want to multiply [tex]\((7x^2 + 9x + 7)(9x - 4)\)[/tex].
### Step 1: Distribute each term in the first polynomial to each term in the second polynomial
Multiply the first term of the first polynomial by each term of the second polynomial:
- [tex]\(7x^2 \cdot 9x = 63x^3\)[/tex]
- [tex]\(7x^2 \cdot (-4) = -28x^2\)[/tex]
Multiply the second term of the first polynomial by each term of the second polynomial:
- [tex]\(9x \cdot 9x = 81x^2\)[/tex]
- [tex]\(9x \cdot (-4) = -36x\)[/tex]
Multiply the third term of the first polynomial by each term of the second polynomial:
- [tex]\(7 \cdot 9x = 63x\)[/tex]
- [tex]\(7 \cdot (-4) = -28\)[/tex]
### Step 2: Combine all the results
Now, we combine all these results together:
- [tex]\(63x^3\)[/tex]
- [tex]\(-28x^2 + 81x^2 = 53x^2\)[/tex]
- [tex]\(-36x + 63x = 27x\)[/tex]
- [tex]\(-28\)[/tex]
### Step 3: Write the final polynomial
So, after combining all like terms, the resulting polynomial is:
[tex]\[ 63x^3 + 53x^2 + 27x - 28 \][/tex]
From the given options, the correct answer is:
D. [tex]\(63x^3 + 53x^2 + 27x - 28\)[/tex]
We want to multiply [tex]\((7x^2 + 9x + 7)(9x - 4)\)[/tex].
### Step 1: Distribute each term in the first polynomial to each term in the second polynomial
Multiply the first term of the first polynomial by each term of the second polynomial:
- [tex]\(7x^2 \cdot 9x = 63x^3\)[/tex]
- [tex]\(7x^2 \cdot (-4) = -28x^2\)[/tex]
Multiply the second term of the first polynomial by each term of the second polynomial:
- [tex]\(9x \cdot 9x = 81x^2\)[/tex]
- [tex]\(9x \cdot (-4) = -36x\)[/tex]
Multiply the third term of the first polynomial by each term of the second polynomial:
- [tex]\(7 \cdot 9x = 63x\)[/tex]
- [tex]\(7 \cdot (-4) = -28\)[/tex]
### Step 2: Combine all the results
Now, we combine all these results together:
- [tex]\(63x^3\)[/tex]
- [tex]\(-28x^2 + 81x^2 = 53x^2\)[/tex]
- [tex]\(-36x + 63x = 27x\)[/tex]
- [tex]\(-28\)[/tex]
### Step 3: Write the final polynomial
So, after combining all like terms, the resulting polynomial is:
[tex]\[ 63x^3 + 53x^2 + 27x - 28 \][/tex]
From the given options, the correct answer is:
D. [tex]\(63x^3 + 53x^2 + 27x - 28\)[/tex]
