Answer :
Certainly! Let's multiply the expressions [tex]\((x^4 + 1)\)[/tex] and [tex]\((3x^2 + 9x + 2)\)[/tex] step by step.
Step 1: Distribute [tex]\(x^4\)[/tex] from the first expression
- Multiply [tex]\(x^4\)[/tex] by each term in the second expression:
[tex]\[
x^4 \cdot 3x^2 = 3x^6
\][/tex]
[tex]\[
x^4 \cdot 9x = 9x^5
\][/tex]
[tex]\[
x^4 \cdot 2 = 2x^4
\][/tex]
Step 2: Distribute [tex]\(1\)[/tex] from the first expression
- Multiply [tex]\(1\)[/tex] by each term in the second expression:
[tex]\[
1 \cdot 3x^2 = 3x^2
\][/tex]
[tex]\[
1 \cdot 9x = 9x
\][/tex]
[tex]\[
1 \cdot 2 = 2
\][/tex]
Step 3: Combine all the products
- List all the terms obtained from both distributive steps:
[tex]\[
3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2
\][/tex]
This is the expanded form of the product [tex]\((x^4 + 1)(3x^2 + 9x + 2)\)[/tex].
So, the final result is:
[tex]\[ 3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2 \][/tex]
That's the solution!
Step 1: Distribute [tex]\(x^4\)[/tex] from the first expression
- Multiply [tex]\(x^4\)[/tex] by each term in the second expression:
[tex]\[
x^4 \cdot 3x^2 = 3x^6
\][/tex]
[tex]\[
x^4 \cdot 9x = 9x^5
\][/tex]
[tex]\[
x^4 \cdot 2 = 2x^4
\][/tex]
Step 2: Distribute [tex]\(1\)[/tex] from the first expression
- Multiply [tex]\(1\)[/tex] by each term in the second expression:
[tex]\[
1 \cdot 3x^2 = 3x^2
\][/tex]
[tex]\[
1 \cdot 9x = 9x
\][/tex]
[tex]\[
1 \cdot 2 = 2
\][/tex]
Step 3: Combine all the products
- List all the terms obtained from both distributive steps:
[tex]\[
3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2
\][/tex]
This is the expanded form of the product [tex]\((x^4 + 1)(3x^2 + 9x + 2)\)[/tex].
So, the final result is:
[tex]\[ 3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2 \][/tex]
That's the solution!
