Answer :
Sure! Let's go through the multiplication of the polynomials step-by-step.
We need to multiply the polynomials [tex]\((7x^2 + 9x + 7)\)[/tex] and [tex]\((9x - 4)\)[/tex].
Step 1: Use the distributive property to multiply each term in the first polynomial by each term in the second polynomial. This will look like:
1. Multiply [tex]\(7x^2\)[/tex] by [tex]\((9x - 4)\)[/tex]:
[tex]\[
7x^2 \cdot 9x = 63x^3
\][/tex]
[tex]\[
7x^2 \cdot (-4) = -28x^2
\][/tex]
2. Multiply [tex]\(9x\)[/tex] by [tex]\((9x - 4)\)[/tex]:
[tex]\[
9x \cdot 9x = 81x^2
\][/tex]
[tex]\[
9x \cdot (-4) = -36x
\][/tex]
3. Multiply [tex]\(7\)[/tex] by [tex]\((9x - 4)\)[/tex]:
[tex]\[
7 \cdot 9x = 63x
\][/tex]
[tex]\[
7 \cdot (-4) = -28
\][/tex]
Step 2: Combine all these results:
- From the previous calculations, we have:
[tex]\[
63x^3 + (-28x^2) + 81x^2 + (-36x) + 63x + (-28)
\][/tex]
Step 3: Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(-28x^2 + 81x^2 = 53x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-36x + 63x = 27x\)[/tex]
Putting it all together, the simplified polynomial is:
[tex]\[
63x^3 + 53x^2 + 27x - 28
\][/tex]
So, the correct answer is Option A: [tex]\(63x^3 + 53x^2 + 27x - 28\)[/tex].
We need to multiply the polynomials [tex]\((7x^2 + 9x + 7)\)[/tex] and [tex]\((9x - 4)\)[/tex].
Step 1: Use the distributive property to multiply each term in the first polynomial by each term in the second polynomial. This will look like:
1. Multiply [tex]\(7x^2\)[/tex] by [tex]\((9x - 4)\)[/tex]:
[tex]\[
7x^2 \cdot 9x = 63x^3
\][/tex]
[tex]\[
7x^2 \cdot (-4) = -28x^2
\][/tex]
2. Multiply [tex]\(9x\)[/tex] by [tex]\((9x - 4)\)[/tex]:
[tex]\[
9x \cdot 9x = 81x^2
\][/tex]
[tex]\[
9x \cdot (-4) = -36x
\][/tex]
3. Multiply [tex]\(7\)[/tex] by [tex]\((9x - 4)\)[/tex]:
[tex]\[
7 \cdot 9x = 63x
\][/tex]
[tex]\[
7 \cdot (-4) = -28
\][/tex]
Step 2: Combine all these results:
- From the previous calculations, we have:
[tex]\[
63x^3 + (-28x^2) + 81x^2 + (-36x) + 63x + (-28)
\][/tex]
Step 3: Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(-28x^2 + 81x^2 = 53x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(-36x + 63x = 27x\)[/tex]
Putting it all together, the simplified polynomial is:
[tex]\[
63x^3 + 53x^2 + 27x - 28
\][/tex]
So, the correct answer is Option A: [tex]\(63x^3 + 53x^2 + 27x - 28\)[/tex].
