Answer :
Sure! Let's find the product of [tex]\(2x^4(4x^2 + 3x + 1)\)[/tex] step-by-step:
1. Distribute [tex]\(2x^4\)[/tex]:
We need to multiply each term inside the parentheses by [tex]\(2x^4\)[/tex].
- First Term: Multiply [tex]\(2x^4\)[/tex] by [tex]\(4x^2\)[/tex].
[tex]\[
2x^4 \times 4x^2 = 8x^{4+2} = 8x^6
\][/tex]
- Second Term: Multiply [tex]\(2x^4\)[/tex] by [tex]\(3x\)[/tex].
[tex]\[
2x^4 \times 3x = 6x^{4+1} = 6x^5
\][/tex]
- Third Term: Multiply [tex]\(2x^4\)[/tex] by [tex]\(1\)[/tex].
[tex]\[
2x^4 \times 1 = 2x^4
\][/tex]
2. Combine the Results:
Now, we combine all the terms we calculated:
[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].
Thus, among the given choices, the correct answer is:
[tex]\(8x^6 + 6x^5 + 2x^4\)[/tex]
1. Distribute [tex]\(2x^4\)[/tex]:
We need to multiply each term inside the parentheses by [tex]\(2x^4\)[/tex].
- First Term: Multiply [tex]\(2x^4\)[/tex] by [tex]\(4x^2\)[/tex].
[tex]\[
2x^4 \times 4x^2 = 8x^{4+2} = 8x^6
\][/tex]
- Second Term: Multiply [tex]\(2x^4\)[/tex] by [tex]\(3x\)[/tex].
[tex]\[
2x^4 \times 3x = 6x^{4+1} = 6x^5
\][/tex]
- Third Term: Multiply [tex]\(2x^4\)[/tex] by [tex]\(1\)[/tex].
[tex]\[
2x^4 \times 1 = 2x^4
\][/tex]
2. Combine the Results:
Now, we combine all the terms we calculated:
[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].
Thus, among the given choices, the correct answer is:
[tex]\(8x^6 + 6x^5 + 2x^4\)[/tex]
