Answer :
To find the product of the expression [tex]\(2x^4(4x^2 + 3x + 1)\)[/tex], we can use distribution to expand the expression. Here are the steps broken down:
1. Distribute [tex]\(2x^4\)[/tex] to each term inside the parentheses:
- First, we multiply [tex]\(2x^4\)[/tex] by [tex]\(4x^2\)[/tex]:
[tex]\[
2x^4 \times 4x^2 = 8x^6
\][/tex]
- Next, we multiply [tex]\(2x^4\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
2x^4 \times 3x = 6x^5
\][/tex]
- Finally, we multiply [tex]\(2x^4\)[/tex] by [tex]\(1\)[/tex]:
[tex]\[
2x^4 \times 1 = 2x^4
\][/tex]
2. Combine the terms:
- After distributing, we collect all the multiplied terms together to form the final expression:
[tex]\[
8x^6 + 6x^5 + 2x^4
\][/tex]
The expanded expression is [tex]\(8x^6 + 6x^5 + 2x^4\)[/tex].
Thus, the product of [tex]\(2x^4(4x^2 + 3x + 1)\)[/tex] is [tex]\(8x^6 + 6x^5 + 2x^4\)[/tex].
1. Distribute [tex]\(2x^4\)[/tex] to each term inside the parentheses:
- First, we multiply [tex]\(2x^4\)[/tex] by [tex]\(4x^2\)[/tex]:
[tex]\[
2x^4 \times 4x^2 = 8x^6
\][/tex]
- Next, we multiply [tex]\(2x^4\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
2x^4 \times 3x = 6x^5
\][/tex]
- Finally, we multiply [tex]\(2x^4\)[/tex] by [tex]\(1\)[/tex]:
[tex]\[
2x^4 \times 1 = 2x^4
\][/tex]
2. Combine the terms:
- After distributing, we collect all the multiplied terms together to form the final expression:
[tex]\[
8x^6 + 6x^5 + 2x^4
\][/tex]
The expanded expression is [tex]\(8x^6 + 6x^5 + 2x^4\)[/tex].
Thus, the product of [tex]\(2x^4(4x^2 + 3x + 1)\)[/tex] is [tex]\(8x^6 + 6x^5 + 2x^4\)[/tex].
