High School

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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 expressions [tex]\((x^4 + 1)\)[/tex] and [tex]\((3x^2 + 9x + 2)\)[/tex] step by step.

### Step 1: Distribute Each Term

We will use the distributive property to multiply each term in [tex]\((x^4 + 1)\)[/tex] by each term in [tex]\((3x^2 + 9x + 2)\)[/tex].

#### Multiply [tex]\(x^4\)[/tex] by Each Term in [tex]\((3x^2 + 9x + 2)\)[/tex]:

1. [tex]\(x^4 \times 3x^2 = 3x^{6}\)[/tex]
2. [tex]\(x^4 \times 9x = 9x^{5}\)[/tex]
3. [tex]\(x^4 \times 2 = 2x^{4}\)[/tex]

#### Multiply [tex]\(1\)[/tex] by Each Term in [tex]\((3x^2 + 9x + 2)\)[/tex]:

1. [tex]\(1 \times 3x^2 = 3x^{2}\)[/tex]
2. [tex]\(1 \times 9x = 9x\)[/tex]
3. [tex]\(1 \times 2 = 2\)[/tex]

### Step 2: Combine All Terms

Now, we combine all the products we obtained:

[tex]\[
3x^{6} + 9x^{5} + 2x^{4} + 3x^{2} + 9x + 2
\][/tex]

These are all the terms we obtained from distributing. Now we organize these terms in descending order of exponents:

### Final Answer:

The result of multiplying [tex]\((x^4 + 1)\)[/tex] by [tex]\((3x^2 + 9x + 2)\)[/tex] is:

[tex]\[3x^{6} + 9x^{5} + 2x^{4} + 3x^{2} + 9x + 2\][/tex]

And that's your expanded expression!

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