Answer :
To find the product of [tex]\(2x^4(4x^2 + 3x + 1)\)[/tex], we need to distribute [tex]\(2x^4\)[/tex] across the terms inside the parentheses. Here's how it's done step-by-step:
1. Distribute [tex]\(2x^4\)[/tex] to each term inside the parentheses:
- First, multiply [tex]\(2x^4\)[/tex] by [tex]\(4x^2\)[/tex]:
[tex]\[
2x^4 \cdot 4x^2 = 8x^{4+2} = 8x^6
\][/tex]
- Next, multiply [tex]\(2x^4\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
2x^4 \cdot 3x = 6x^{4+1} = 6x^5
\][/tex]
- Finally, multiply [tex]\(2x^4\)[/tex] by [tex]\(1\)[/tex]:
[tex]\[
2x^4 \cdot 1 = 2x^4
\][/tex]
2. Combine all the results:
By adding the results of these multiplications, we get:
[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 each term inside the parentheses:
- First, multiply [tex]\(2x^4\)[/tex] by [tex]\(4x^2\)[/tex]:
[tex]\[
2x^4 \cdot 4x^2 = 8x^{4+2} = 8x^6
\][/tex]
- Next, multiply [tex]\(2x^4\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
2x^4 \cdot 3x = 6x^{4+1} = 6x^5
\][/tex]
- Finally, multiply [tex]\(2x^4\)[/tex] by [tex]\(1\)[/tex]:
[tex]\[
2x^4 \cdot 1 = 2x^4
\][/tex]
2. Combine all the results:
By adding the results of these multiplications, we get:
[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].
