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Find the product of [tex]2x^4(4x^2+3x+1)[/tex].

A. [tex]8x^6 + 6x^5 + 2x^4[/tex]

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

C. [tex]2x^4 + 6x^5 + 8x^6[/tex]

D. [tex]6x^6 + 5x^5 + 3x^4[/tex]

Answer :

To find the product of [tex]\(2x^4(4x^2 + 3x + 1)\)[/tex], we will distribute [tex]\(2x^4\)[/tex] to each term inside the parentheses. Here is the step-by-step solution:

1. Distribute [tex]\(2x^4\)[/tex] to [tex]\(4x^2\)[/tex]:
[tex]\[
2x^4 \times 4x^2 = 8x^{(4+2)} = 8x^6
\][/tex]

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

3. Distribute [tex]\(2x^4\)[/tex] to [tex]\(1\)[/tex]:
[tex]\[
2x^4 \times 1 = 2x^4
\][/tex]

4. Add the resulting terms together:
[tex]\[
8x^6 + 6x^5 + 2x^4
\][/tex]

So, the product of [tex]\(2x^4(4x^2 + 3x + 1)\)[/tex] is [tex]\(8x^6 + 6x^5 + 2x^4\)[/tex].

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