Answer :
To find the product of [tex]\(2x^4(4x^2 + 3x + 1)\)[/tex], we will distribute [tex]\(2x^4\)[/tex] to each term inside the parentheses. Here is the step-by-step solution:
1. Distribute [tex]\(2x^4\)[/tex] to [tex]\(4x^2\)[/tex]:
[tex]\[
2x^4 \times 4x^2 = 8x^{(4+2)} = 8x^6
\][/tex]
2. Distribute [tex]\(2x^4\)[/tex] to [tex]\(3x\)[/tex]:
[tex]\[
2x^4 \times 3x = 6x^{(4+1)} = 6x^5
\][/tex]
3. Distribute [tex]\(2x^4\)[/tex] to [tex]\(1\)[/tex]:
[tex]\[
2x^4 \times 1 = 2x^4
\][/tex]
4. Add the resulting terms together:
[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].
1. Distribute [tex]\(2x^4\)[/tex] to [tex]\(4x^2\)[/tex]:
[tex]\[
2x^4 \times 4x^2 = 8x^{(4+2)} = 8x^6
\][/tex]
2. Distribute [tex]\(2x^4\)[/tex] to [tex]\(3x\)[/tex]:
[tex]\[
2x^4 \times 3x = 6x^{(4+1)} = 6x^5
\][/tex]
3. Distribute [tex]\(2x^4\)[/tex] to [tex]\(1\)[/tex]:
[tex]\[
2x^4 \times 1 = 2x^4
\][/tex]
4. Add the resulting terms together:
[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].
