To find the product of [tex]\(2 x^4 (2 x^2 + 3 x + 4)\)[/tex], we will expand the expression step-by-step.
1. Distribute [tex]\(2 x^4\)[/tex] to each term inside the parentheses:
[tex]\[
2 x^4 (2 x^2 + 3 x + 4)
\][/tex]
2. Multiply [tex]\(2 x^4\)[/tex] by each term in [tex]\(2 x^2 + 3 x + 4\)[/tex]:
[tex]\[
2 x^4 \cdot 2 x^2 + 2 x^4 \cdot 3 x + 2 x^4 \cdot 4
\][/tex]
3. Perform each multiplication:
[tex]\[
2 x^4 \cdot 2 x^2 = 4 x^6
\][/tex]
[tex]\[
2 x^4 \cdot 3 x = 6 x^5
\][/tex]
[tex]\[
2 x^4 \cdot 4 = 8 x^4
\][/tex]
4. Combine all the terms obtained:
[tex]\[
4 x^6 + 6 x^5 + 8 x^4
\][/tex]
Thus, the expanded expression is:
[tex]\[
4 x^6 + 6 x^5 + 8 x^4
\][/tex]
By comparing this result with the given choices, we see that the correct answer is:
[tex]\[
4 x^6 + 6 x^5 + 8 x^4
\][/tex]
Therefore, the correct choice is:
[tex]\[
4 x^6 + 6 x^5 + 8 x^4
\][/tex]
