College

Select the simplified form of this expression:

[tex]2x^4(x^2+5)[/tex]

A. [tex]2x^8+7x^4[/tex]
B. [tex]10x^6[/tex]
C. [tex]2x^8+10x^4[/tex]
D. [tex]2x^6+10x^4[/tex]
E. [tex]2x^6+7x^4[/tex]

Answer :

To simplify the expression [tex]\(2x^4(x^2+5)\)[/tex], we need to distribute [tex]\(2x^4\)[/tex] across the terms inside the parenthesis. Let's go through the steps:

1. Identify the terms to distribute: We have an expression [tex]\(2x^4(x^2 + 5)\)[/tex], and we need to distribute [tex]\(2x^4\)[/tex] to both [tex]\(x^2\)[/tex] and [tex]\(5\)[/tex].

2. Distribute [tex]\(2x^4\)[/tex] across [tex]\(x^2\)[/tex]:
[tex]\[
2x^4 \cdot x^2 = 2x^{4+2} = 2x^6
\][/tex]
When you multiply powers of [tex]\(x\)[/tex], you add the exponents together.

3. Distribute [tex]\(2x^4\)[/tex] across [tex]\(5\)[/tex]:
[tex]\[
2x^4 \cdot 5 = 10x^4
\][/tex]
Here, multiply the numerical coefficients (2 and 5), and keep the [tex]\(x^4\)[/tex] as it is.

4. Combine the results:
[tex]\[
2x^6 + 10x^4
\][/tex]
This is the expression after full distribution.

Therefore, the simplified form of the expression is [tex]\(\boxed{2x^6 + 10x^4}\)[/tex]. This matches with option C from the choices provided.