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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.
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.
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