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Answer :
Sure! To solve the problem of multiplying the two expressions [tex]\((x^4 + 1)\)[/tex] and [tex]\((3x^2 + 9x + 2)\)[/tex], we can use the distributive property to expand the expressions step by step. Here's how you do it:
1. Distribute each term in the first expression [tex]\((x^4 + 1)\)[/tex] to every term in the second expression [tex]\((3x^2 + 9x + 2)\)[/tex].
2. Start by distributing [tex]\(x^4\)[/tex] across the terms in [tex]\((3x^2 + 9x + 2)\)[/tex]:
- Multiply [tex]\(x^4\)[/tex] by [tex]\(3x^2\)[/tex]: [tex]\(x^4 \times 3x^2 = 3x^6\)[/tex]
- Multiply [tex]\(x^4\)[/tex] by [tex]\(9x\)[/tex]: [tex]\(x^4 \times 9x = 9x^5\)[/tex]
- Multiply [tex]\(x^4\)[/tex] by [tex]\(2\)[/tex]: [tex]\(x^4 \times 2 = 2x^4\)[/tex]
3. Now distribute [tex]\(1\)[/tex] across the terms in [tex]\((3x^2 + 9x + 2)\)[/tex]:
- Multiply [tex]\(1\)[/tex] by [tex]\(3x^2\)[/tex]: [tex]\(1 \times 3x^2 = 3x^2\)[/tex]
- Multiply [tex]\(1\)[/tex] by [tex]\(9x\)[/tex]: [tex]\(1 \times 9x = 9x\)[/tex]
- Multiply [tex]\(1\)[/tex] by [tex]\(2\)[/tex]: [tex]\(1 \times 2 = 2\)[/tex]
4. Combine all the products:
- [tex]\(3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2\)[/tex]
So, the expanded result of multiplying the two expressions is:
[tex]\[3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2\][/tex]
This is your final answer!
1. Distribute each term in the first expression [tex]\((x^4 + 1)\)[/tex] to every term in the second expression [tex]\((3x^2 + 9x + 2)\)[/tex].
2. Start by distributing [tex]\(x^4\)[/tex] across the terms in [tex]\((3x^2 + 9x + 2)\)[/tex]:
- Multiply [tex]\(x^4\)[/tex] by [tex]\(3x^2\)[/tex]: [tex]\(x^4 \times 3x^2 = 3x^6\)[/tex]
- Multiply [tex]\(x^4\)[/tex] by [tex]\(9x\)[/tex]: [tex]\(x^4 \times 9x = 9x^5\)[/tex]
- Multiply [tex]\(x^4\)[/tex] by [tex]\(2\)[/tex]: [tex]\(x^4 \times 2 = 2x^4\)[/tex]
3. Now distribute [tex]\(1\)[/tex] across the terms in [tex]\((3x^2 + 9x + 2)\)[/tex]:
- Multiply [tex]\(1\)[/tex] by [tex]\(3x^2\)[/tex]: [tex]\(1 \times 3x^2 = 3x^2\)[/tex]
- Multiply [tex]\(1\)[/tex] by [tex]\(9x\)[/tex]: [tex]\(1 \times 9x = 9x\)[/tex]
- Multiply [tex]\(1\)[/tex] by [tex]\(2\)[/tex]: [tex]\(1 \times 2 = 2\)[/tex]
4. Combine all the products:
- [tex]\(3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2\)[/tex]
So, the expanded result of multiplying the two expressions is:
[tex]\[3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2\][/tex]
This is your final answer!
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