College

Multiply:

[tex]\left(x^4 + 1\right)\left(3x^2 + 9x + 2\right)[/tex]

A. [tex]x^4 + 3x^2 + 9x + 3[/tex]

B. [tex]3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2[/tex]

C. [tex]3x^7 + 9x^6 + 2x^5[/tex]

D. [tex]3x^8 + 9x^4 + 2x^4 + 3x^2 + 9x + 2[/tex]

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.