Answer :
Let's find the product of the expression [tex]\(2x^4(2x^2 + 3x + 4)\)[/tex] by distributing [tex]\(2x^4\)[/tex] through the polynomial inside the parentheses. Here's a step-by-step breakdown:
1. Distribute [tex]\(2x^4\)[/tex] to [tex]\(2x^2\)[/tex]:
[tex]\[
2x^4 \cdot 2x^2 = 4x^{4+2} = 4x^6
\][/tex]
2. Distribute [tex]\(2x^4\)[/tex] to [tex]\(3x\)[/tex]:
[tex]\[
2x^4 \cdot 3x = 6x^{4+1} = 6x^5
\][/tex]
3. Distribute [tex]\(2x^4\)[/tex] to [tex]\(4\)[/tex]:
[tex]\[
2x^4 \cdot 4 = 8x^4
\][/tex]
Now, combine all these terms to get the final expanded expression:
[tex]\[
4x^6 + 6x^5 + 8x^4
\][/tex]
Therefore, the correct product is [tex]\(4x^6 + 6x^5 + 8x^4\)[/tex]. This matches the option [tex]\(4 x^6 + 6 x^5 + 8 x^4\)[/tex].
1. Distribute [tex]\(2x^4\)[/tex] to [tex]\(2x^2\)[/tex]:
[tex]\[
2x^4 \cdot 2x^2 = 4x^{4+2} = 4x^6
\][/tex]
2. Distribute [tex]\(2x^4\)[/tex] to [tex]\(3x\)[/tex]:
[tex]\[
2x^4 \cdot 3x = 6x^{4+1} = 6x^5
\][/tex]
3. Distribute [tex]\(2x^4\)[/tex] to [tex]\(4\)[/tex]:
[tex]\[
2x^4 \cdot 4 = 8x^4
\][/tex]
Now, combine all these terms to get the final expanded expression:
[tex]\[
4x^6 + 6x^5 + 8x^4
\][/tex]
Therefore, the correct product is [tex]\(4x^6 + 6x^5 + 8x^4\)[/tex]. This matches the option [tex]\(4 x^6 + 6 x^5 + 8 x^4\)[/tex].
