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Simplify the expression:

[tex]14 x^5 \left(13 x^2 + 13 x^5\right)[/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 :

Sure, let's solve the given expression step-by-step.

The given expression is:
[tex]\[ 14 x^5 \left( 13 x^2 + 13 x^5 \right) \][/tex]

First, let's distribute [tex]\( 14 x^5 \)[/tex] across the terms inside the parentheses.

1. Distribute [tex]\( 14 x^5 \)[/tex] to [tex]\( 13 x^2 \)[/tex]:
[tex]\[ 14 x^5 \cdot 13 x^2 = 14 \cdot 13 \cdot x^{5 + 2} = 182 x^7 \][/tex]

2. Distribute [tex]\( 14 x^5 \)[/tex] to [tex]\( 13 x^5 \)[/tex]:
[tex]\[ 14 x^5 \cdot 13 x^5 = 14 \cdot 13 \cdot x^{5 + 5} = 182 x^{10} \][/tex]

After distributing, we add the two terms together:
[tex]\[ 182 x^7 + 182 x^{10} \][/tex]

So the correct answer is:
[tex]\[ \boxed{c. 182 x^7 + 182 x^{10}} \][/tex]

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