Answer :
To multiply the expressions [tex]\((x^4 + 1)\)[/tex] and [tex]\((3x^2 + 9x + 2)\)[/tex], we'll distribute each term in the first expression by each term in the second expression. Let's break it down step by step:
1. Distribute [tex]\(x^4\)[/tex]:
- [tex]\(x^4 \times 3x^2 = 3x^{6}\)[/tex]
- [tex]\(x^4 \times 9x = 9x^{5}\)[/tex]
- [tex]\(x^4 \times 2 = 2x^{4}\)[/tex]
2. Distribute [tex]\(1\)[/tex]:
- [tex]\(1 \times 3x^2 = 3x^2\)[/tex]
- [tex]\(1 \times 9x = 9x\)[/tex]
- [tex]\(1 \times 2 = 2\)[/tex]
Now, combine all these results:
[tex]\[
3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2
\][/tex]
The expression is already in its expanded form. There are no like terms to combine here, so this is the final answer.
1. Distribute [tex]\(x^4\)[/tex]:
- [tex]\(x^4 \times 3x^2 = 3x^{6}\)[/tex]
- [tex]\(x^4 \times 9x = 9x^{5}\)[/tex]
- [tex]\(x^4 \times 2 = 2x^{4}\)[/tex]
2. Distribute [tex]\(1\)[/tex]:
- [tex]\(1 \times 3x^2 = 3x^2\)[/tex]
- [tex]\(1 \times 9x = 9x\)[/tex]
- [tex]\(1 \times 2 = 2\)[/tex]
Now, combine all these results:
[tex]\[
3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2
\][/tex]
The expression is already in its expanded form. There are no like terms to combine here, so this is the final answer.
