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Answer :
Sure! Let's multiply the two expressions step by step: [tex]\((x^4 + 1)(3x^2 + 9x + 2)\)[/tex].
1. Distribute [tex]\(x^4\)[/tex] to 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]
After this step, we have: [tex]\(3x^6 + 9x^5 + 2x^4\)[/tex].
2. Distribute [tex]\(1\)[/tex] to 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]
After this step, we have: [tex]\(3x^2 + 9x + 2\)[/tex].
3. Combine all terms:
Now, add all the expanded terms together.
- From step 1: [tex]\(3x^6 + 9x^5 + 2x^4\)[/tex]
- From step 2: [tex]\(3x^2 + 9x + 2\)[/tex]
So, the result is:
[tex]\[
3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2
\][/tex]
This is the final result after multiplying the given expressions.
1. Distribute [tex]\(x^4\)[/tex] to 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]
After this step, we have: [tex]\(3x^6 + 9x^5 + 2x^4\)[/tex].
2. Distribute [tex]\(1\)[/tex] to 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]
After this step, we have: [tex]\(3x^2 + 9x + 2\)[/tex].
3. Combine all terms:
Now, add all the expanded terms together.
- From step 1: [tex]\(3x^6 + 9x^5 + 2x^4\)[/tex]
- From step 2: [tex]\(3x^2 + 9x + 2\)[/tex]
So, the result is:
[tex]\[
3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2
\][/tex]
This is the final result after multiplying the given expressions.
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