Answer :
To solve the problem of multiplying [tex]\((x^4 + 1)(3x^2 + 9x + 2)\)[/tex], let's break it down into clear, step-by-step parts.
1. Distribute each term in the first expression [tex]\(x^4 + 1\)[/tex] over the second expression [tex]\(3x^2 + 9x + 2\)[/tex].
2. First, distribute [tex]\(x^4\)[/tex]:
- 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]
3. Next, distribute [tex]\(1\)[/tex]:
- 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]
4. Combine all the results:
- After distributing both [tex]\(x^4\)[/tex] and [tex]\(1\)[/tex] over [tex]\(3x^2 + 9x + 2\)[/tex], we add all the terms together:
[tex]\[
3x^{6} + 9x^{5} + 2x^{4} + 3x^{2} + 9x + 2
\][/tex]
Thus, the result of the multiplication is [tex]\(3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2\)[/tex].
1. Distribute each term in the first expression [tex]\(x^4 + 1\)[/tex] over the second expression [tex]\(3x^2 + 9x + 2\)[/tex].
2. First, distribute [tex]\(x^4\)[/tex]:
- 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]
3. Next, distribute [tex]\(1\)[/tex]:
- 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]
4. Combine all the results:
- After distributing both [tex]\(x^4\)[/tex] and [tex]\(1\)[/tex] over [tex]\(3x^2 + 9x + 2\)[/tex], we add all the terms together:
[tex]\[
3x^{6} + 9x^{5} + 2x^{4} + 3x^{2} + 9x + 2
\][/tex]
Thus, the result of the multiplication is [tex]\(3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2\)[/tex].
