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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 the expression [tex]\(2x^4(4x^2 + 3x + 1)\)[/tex], let's multiply each term inside the parentheses by [tex]\(2x^4\)[/tex]. Here's a step-by-step breakdown:

1. Distribute [tex]\(2x^4\)[/tex] to each term inside the parentheses:

- First, multiply [tex]\(2x^4\)[/tex] by [tex]\(4x^2\)[/tex]:
[tex]\[
2x^4 \times 4x^2 = 8x^{4+2} = 8x^6
\][/tex]

- Next, multiply [tex]\(2x^4\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
2x^4 \times 3x = 6x^{4+1} = 6x^5
\][/tex]

- Finally, multiply [tex]\(2x^4\)[/tex] by [tex]\(1\)[/tex]:
[tex]\[
2x^4 \times 1 = 2x^4
\][/tex]

2. Combine all the products:
[tex]\[
8x^6 + 6x^5 + 2x^4
\][/tex]

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

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