Answer :
Sure! Let's solve the problem step-by-step.
We need to find the product of [tex]\(2x^4\)[/tex] and the polynomial [tex]\((4x^2 + 3x + 1)\)[/tex].
To do this, we'll distribute [tex]\(2x^4\)[/tex] across each term in the polynomial:
1. Multiply [tex]\(2x^4\)[/tex] by [tex]\(4x^2\)[/tex]:
[tex]\[
2x^4 \times 4x^2 = 8x^{4+2} = 8x^6
\][/tex]
2. Multiply [tex]\(2x^4\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
2x^4 \times 3x = 6x^{4+1} = 6x^5
\][/tex]
3. Multiply [tex]\(2x^4\)[/tex] by [tex]\(1\)[/tex]:
[tex]\[
2x^4 \times 1 = 2x^4
\][/tex]
Now, we combine all the terms we’ve found:
[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].
This matches with one of the choices: [tex]\(8x^6 + 6x^5 + 2x^4\)[/tex].
We need to find the product of [tex]\(2x^4\)[/tex] and the polynomial [tex]\((4x^2 + 3x + 1)\)[/tex].
To do this, we'll distribute [tex]\(2x^4\)[/tex] across each term in the polynomial:
1. Multiply [tex]\(2x^4\)[/tex] by [tex]\(4x^2\)[/tex]:
[tex]\[
2x^4 \times 4x^2 = 8x^{4+2} = 8x^6
\][/tex]
2. Multiply [tex]\(2x^4\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
2x^4 \times 3x = 6x^{4+1} = 6x^5
\][/tex]
3. Multiply [tex]\(2x^4\)[/tex] by [tex]\(1\)[/tex]:
[tex]\[
2x^4 \times 1 = 2x^4
\][/tex]
Now, we combine all the terms we’ve found:
[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].
This matches with one of the choices: [tex]\(8x^6 + 6x^5 + 2x^4\)[/tex].
