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Answer :
Sure! To multiply the polynomials [tex]\((x^4 + 1)(3x^2 + 9x + 2)\)[/tex], let's go through the process step-by-step.
1. Distribute each term in the first polynomial [tex]\(x^4 + 1\)[/tex] to every term in the second polynomial [tex]\(3x^2 + 9x + 2\)[/tex].
2. Start by distributing [tex]\(x^4\)[/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]
3. Next, distribute [tex]\(1\)[/tex]:
- [tex]\(1 \cdot 3x^2 = 3x^2\)[/tex]
- [tex]\(1 \cdot 9x = 9x\)[/tex]
- [tex]\(1 \cdot 2 = 2\)[/tex]
4. Now, add all these resulting terms together:
[tex]\[
3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2
\][/tex]
5. Combine like terms if there are any. In this case, there are no like terms that need combining.
The multiplied result of [tex]\((x^4 + 1)(3x^2 + 9x + 2)\)[/tex] simplifies to:
[tex]\[
3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2
\][/tex]
So, this is the final answer.
1. Distribute each term in the first polynomial [tex]\(x^4 + 1\)[/tex] to every term in the second polynomial [tex]\(3x^2 + 9x + 2\)[/tex].
2. Start by distributing [tex]\(x^4\)[/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]
3. Next, distribute [tex]\(1\)[/tex]:
- [tex]\(1 \cdot 3x^2 = 3x^2\)[/tex]
- [tex]\(1 \cdot 9x = 9x\)[/tex]
- [tex]\(1 \cdot 2 = 2\)[/tex]
4. Now, add all these resulting terms together:
[tex]\[
3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2
\][/tex]
5. Combine like terms if there are any. In this case, there are no like terms that need combining.
The multiplied result of [tex]\((x^4 + 1)(3x^2 + 9x + 2)\)[/tex] simplifies to:
[tex]\[
3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2
\][/tex]
So, this is the final answer.
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