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Simplify

[tex]14 x^5(13 x^2 + 13 x^5)[/tex]

A. [tex]27 x^{10} + 27 x^{25}[/tex]
B. [tex]182 x^{10} + 13 x^5[/tex]
C. [tex]182 x^7 + 182 x^{10}[/tex]
D. [tex]27 x^7 + 27 x^{10}[/tex]

Answer :

Let's simplify the expression [tex]\(14 x^5\left(13 x^2+13 x^5\right)\)[/tex] step by step.

1. Distribute [tex]\(14 x^5\)[/tex] over the terms inside the parentheses:

- First, multiply [tex]\(14 x^5\)[/tex] by the first term inside the parentheses, which is [tex]\(13 x^2\)[/tex]:
[tex]\[
14 x^5 \cdot 13 x^2 = 182 x^{5+2} = 182 x^7
\][/tex]

- Next, multiply [tex]\(14 x^5\)[/tex] by the second term inside the parentheses, which is [tex]\(13 x^5\)[/tex]:
[tex]\[
14 x^5 \cdot 13 x^5 = 182 x^{5+5} = 182 x^{10}
\][/tex]

2. Combine the results of the multiplication:

After distributing, we combine the products:
[tex]\[
182 x^7 + 182 x^{10}
\][/tex]

The simplified expression is [tex]\(182 x^7 + 182 x^{10}\)[/tex].

Thus, the correct answer is c. [tex]\(182 x^7 + 182 x^{10}\)[/tex].

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