Answer :
To multiply the expressions [tex]\((x^4 + 1)(3x^2 + 9x + 2)\)[/tex], we will apply the distributive property, which involves distributing each term in the first polynomial to each term in the second polynomial.
Let's break this down step-by-step:
1. Start by distributing [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. Next, distribute the constant term [tex]\(1\)[/tex]:
- [tex]\(1 \times 3x^2 = 3x^2\)[/tex]
- [tex]\(1 \times 9x = 9x\)[/tex]
- [tex]\(1 \times 2 = 2\)[/tex]
Now let's combine all these results together:
- From [tex]\(x^4 \times (3x^2 + 9x + 2)\)[/tex], we get: [tex]\(3x^6 + 9x^5 + 2x^4\)[/tex]
- From [tex]\(1 \times (3x^2 + 9x + 2)\)[/tex], we get: [tex]\(3x^2 + 9x + 2\)[/tex]
Finally, add all these terms together:
[tex]\[ 3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2 \][/tex]
This is the expanded form of the original product, [tex]\( (x^4 + 1)(3x^2 + 9x + 2) \)[/tex].
Let's break this down step-by-step:
1. Start by distributing [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. Next, distribute the constant term [tex]\(1\)[/tex]:
- [tex]\(1 \times 3x^2 = 3x^2\)[/tex]
- [tex]\(1 \times 9x = 9x\)[/tex]
- [tex]\(1 \times 2 = 2\)[/tex]
Now let's combine all these results together:
- From [tex]\(x^4 \times (3x^2 + 9x + 2)\)[/tex], we get: [tex]\(3x^6 + 9x^5 + 2x^4\)[/tex]
- From [tex]\(1 \times (3x^2 + 9x + 2)\)[/tex], we get: [tex]\(3x^2 + 9x + 2\)[/tex]
Finally, add all these terms together:
[tex]\[ 3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2 \][/tex]
This is the expanded form of the original product, [tex]\( (x^4 + 1)(3x^2 + 9x + 2) \)[/tex].
