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

A. [tex]$2x^8 + 3x^4 + 4x^4$[/tex]
B. [tex]$4x^6 + 6x^5 + 8x^4$[/tex]
C. [tex]$4x^4 + 3x^5 + 2x^6$[/tex]
D. [tex]$3x^6 + 4x^5 + 5x^4$[/tex]

Answer :

Let's find the product of the expression [tex]\(2x^4(2x^2 + 3x + 4)\)[/tex]. We'll do this by distributing [tex]\(2x^4\)[/tex] to each term inside the parenthesis. Here’s a step-by-step explanation:

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

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

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

- Multiply [tex]\(2x^4\)[/tex] by [tex]\(4\)[/tex]:
[tex]\[
2x^4 \times 4 = 8x^4
\][/tex]

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

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

The correct answer corresponds to option b: [tex]\(4x^6 + 6x^5 + 8x^4\)[/tex].

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