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].
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].
