Answer :
Sure! Let's multiply the polynomials [tex]\((x^4 + 1)\)[/tex] and [tex]\((3x^2 + 9x + 2)\)[/tex] step by step.
1. Distribute each term of [tex]\((x^4 + 1)\)[/tex] to [tex]\((3x^2 + 9x + 2)\)[/tex]:
- First, multiply [tex]\(x^4\)[/tex] by each term in [tex]\((3x^2 + 9x + 2)\)[/tex]:
[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]
- Next, multiply [tex]\(1\)[/tex] by each term in [tex]\((3x^2 + 9x + 2)\)[/tex]:
[tex]\[
1 \cdot 3x^2 = 3x^2
\][/tex]
[tex]\[
1 \cdot 9x = 9x
\][/tex]
[tex]\[
1 \cdot 2 = 2
\][/tex]
2. Combine all the terms:
So, when we combine all these terms, the expanded expression is:
[tex]\[
3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2
\][/tex]
This is the result of multiplying [tex]\((x^4 + 1)\)[/tex] by [tex]\((3x^2 + 9x + 2)\)[/tex].
1. Distribute each term of [tex]\((x^4 + 1)\)[/tex] to [tex]\((3x^2 + 9x + 2)\)[/tex]:
- First, multiply [tex]\(x^4\)[/tex] by each term in [tex]\((3x^2 + 9x + 2)\)[/tex]:
[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]
- Next, multiply [tex]\(1\)[/tex] by each term in [tex]\((3x^2 + 9x + 2)\)[/tex]:
[tex]\[
1 \cdot 3x^2 = 3x^2
\][/tex]
[tex]\[
1 \cdot 9x = 9x
\][/tex]
[tex]\[
1 \cdot 2 = 2
\][/tex]
2. Combine all the terms:
So, when we combine all these terms, the expanded expression is:
[tex]\[
3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2
\][/tex]
This is the result of multiplying [tex]\((x^4 + 1)\)[/tex] by [tex]\((3x^2 + 9x + 2)\)[/tex].
