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Answer :
Let's find the product of the expression [tex]\(2x^4(2x^2 + 3x + 4)\)[/tex].
To do this, we'll distribute the [tex]\(2x^4\)[/tex] to each term within the parentheses:
1. Multiply [tex]\(2x^4\)[/tex] by [tex]\(2x^2\)[/tex]:
[tex]\[
2x^4 \times 2x^2 = 4x^{4+2} = 4x^6
\][/tex]
2. Multiply [tex]\(2x^4\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
2x^4 \times 3x = 6x^{4+1} = 6x^5
\][/tex]
3. Multiply [tex]\(2x^4\)[/tex] by [tex]\(4\)[/tex]:
[tex]\[
2x^4 \times 4 = 8x^{4+0} = 8x^4
\][/tex]
Now, we'll combine the results:
- The product of [tex]\(2x^4\)[/tex] and [tex]\(2x^2\)[/tex] gives us [tex]\(4x^6\)[/tex].
- The product of [tex]\(2x^4\)[/tex] and [tex]\(3x\)[/tex] gives us [tex]\(6x^5\)[/tex].
- The product of [tex]\(2x^4\)[/tex] and [tex]\(4\)[/tex] gives us [tex]\(8x^4\)[/tex].
The resulting expression is:
[tex]\[
4x^6 + 6x^5 + 8x^4
\][/tex]
So, the product of [tex]\(2x^4(2x^2 + 3x + 4)\)[/tex] is [tex]\(4x^6 + 6x^5 + 8x^4\)[/tex].
To do this, we'll distribute the [tex]\(2x^4\)[/tex] to each term within the parentheses:
1. Multiply [tex]\(2x^4\)[/tex] by [tex]\(2x^2\)[/tex]:
[tex]\[
2x^4 \times 2x^2 = 4x^{4+2} = 4x^6
\][/tex]
2. Multiply [tex]\(2x^4\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
2x^4 \times 3x = 6x^{4+1} = 6x^5
\][/tex]
3. Multiply [tex]\(2x^4\)[/tex] by [tex]\(4\)[/tex]:
[tex]\[
2x^4 \times 4 = 8x^{4+0} = 8x^4
\][/tex]
Now, we'll combine the results:
- The product of [tex]\(2x^4\)[/tex] and [tex]\(2x^2\)[/tex] gives us [tex]\(4x^6\)[/tex].
- The product of [tex]\(2x^4\)[/tex] and [tex]\(3x\)[/tex] gives us [tex]\(6x^5\)[/tex].
- The product of [tex]\(2x^4\)[/tex] and [tex]\(4\)[/tex] gives us [tex]\(8x^4\)[/tex].
The resulting expression is:
[tex]\[
4x^6 + 6x^5 + 8x^4
\][/tex]
So, the product of [tex]\(2x^4(2x^2 + 3x + 4)\)[/tex] is [tex]\(4x^6 + 6x^5 + 8x^4\)[/tex].
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