Answer :
Sure! Let's find the product of the expression [tex]\(2x^4(2x^2 + 3x + 4)\)[/tex].
We begin by distributing [tex]\(2x^4\)[/tex] to each term within the parentheses:
1. First term: Multiply [tex]\(2x^4\)[/tex] by [tex]\(2x^2\)[/tex]:
[tex]\[
2x^4 \times 2x^2 = 4x^{4+2} = 4x^6
\][/tex]
2. Second term: Multiply [tex]\(2x^4\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
2x^4 \times 3x = 6x^{4+1} = 6x^5
\][/tex]
3. Third term: Multiply [tex]\(2x^4\)[/tex] by [tex]\(4\)[/tex]:
[tex]\[
2x^4 \times 4 = 8x^4
\][/tex]
Finally, we combine all the results from the multiplication to get the expanded expression:
[tex]\[
4x^6 + 6x^5 + 8x^4
\][/tex]
Therefore, the correct product of the expression is [tex]\(4x^6 + 6x^5 + 8x^4\)[/tex], which corresponds to option b.
We begin by distributing [tex]\(2x^4\)[/tex] to each term within the parentheses:
1. First term: Multiply [tex]\(2x^4\)[/tex] by [tex]\(2x^2\)[/tex]:
[tex]\[
2x^4 \times 2x^2 = 4x^{4+2} = 4x^6
\][/tex]
2. Second term: Multiply [tex]\(2x^4\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
2x^4 \times 3x = 6x^{4+1} = 6x^5
\][/tex]
3. Third term: Multiply [tex]\(2x^4\)[/tex] by [tex]\(4\)[/tex]:
[tex]\[
2x^4 \times 4 = 8x^4
\][/tex]
Finally, we combine all the results from the multiplication to get the expanded expression:
[tex]\[
4x^6 + 6x^5 + 8x^4
\][/tex]
Therefore, the correct product of the expression is [tex]\(4x^6 + 6x^5 + 8x^4\)[/tex], which corresponds to option b.
