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Answer :
Sure! Let's find the product of [tex]\(2x^4\)[/tex] and the polynomial [tex]\((2x^2 + 3x + 4)\)[/tex].
Here is how you can do it step-by-step:
1. Distribute [tex]\(2x^4\)[/tex] to each term inside the parentheses [tex]\((2x^2 + 3x + 4)\)[/tex].
- Multiply [tex]\(2x^4\)[/tex] with [tex]\(2x^2\)[/tex]:
[tex]\[
2x^4 \times 2x^2 = 4x^{4+2} = 4x^6
\][/tex]
- Multiply [tex]\(2x^4\)[/tex] with [tex]\(3x\)[/tex]:
[tex]\[
2x^4 \times 3x = 6x^{4+1} = 6x^5
\][/tex]
- Multiply [tex]\(2x^4\)[/tex] with [tex]\(4\)[/tex]:
[tex]\[
2x^4 \times 4 = 8x^4
\][/tex]
2. Combine all the products into a single expression:
[tex]\[
4x^6 + 6x^5 + 8x^4
\][/tex]
So, the product of [tex]\(2x^4(2x^2 + 3x + 4)\)[/tex] is [tex]\(4x^6 + 6x^5 + 8x^4\)[/tex].
The correct option from the given list is:
[tex]\[ 4x^6 + 6x^5 + 8x^4 \][/tex]
Here is how you can do it step-by-step:
1. Distribute [tex]\(2x^4\)[/tex] to each term inside the parentheses [tex]\((2x^2 + 3x + 4)\)[/tex].
- Multiply [tex]\(2x^4\)[/tex] with [tex]\(2x^2\)[/tex]:
[tex]\[
2x^4 \times 2x^2 = 4x^{4+2} = 4x^6
\][/tex]
- Multiply [tex]\(2x^4\)[/tex] with [tex]\(3x\)[/tex]:
[tex]\[
2x^4 \times 3x = 6x^{4+1} = 6x^5
\][/tex]
- Multiply [tex]\(2x^4\)[/tex] with [tex]\(4\)[/tex]:
[tex]\[
2x^4 \times 4 = 8x^4
\][/tex]
2. Combine all the products into a single expression:
[tex]\[
4x^6 + 6x^5 + 8x^4
\][/tex]
So, the product of [tex]\(2x^4(2x^2 + 3x + 4)\)[/tex] is [tex]\(4x^6 + 6x^5 + 8x^4\)[/tex].
The correct option from the given list is:
[tex]\[ 4x^6 + 6x^5 + 8x^4 \][/tex]
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