Certainly! Let's simplify the given expression step by step.
We start with the given expression:
[tex]\[
14 x^5 \left( 13 x^2 + 13 x^5 \right)
\][/tex]
First, we distribute [tex]\( 14 x^5 \)[/tex] across the terms inside the parentheses:
[tex]\[
14 x^5 \cdot 13 x^2 + 14 x^5 \cdot 13 x^5
\][/tex]
Next, we perform the multiplication in each term individually:
1. For the first term:
[tex]\[
14 x^5 \cdot 13 x^2 = (14 \cdot 13) x^{5+2} = 182 x^7
\][/tex]
2. For the second term:
[tex]\[
14 x^5 \cdot 13 x^5 = (14 \cdot 13) x^{5+5} = 182 x^{10}
\][/tex]
Thus, after simplifying both terms, we get:
[tex]\[
182 x^7 + 182 x^{10}
\][/tex]
Now, we notice that both terms have a common factor of [tex]\( 182 x^7 \)[/tex]. Thus, we can factor out [tex]\( 182 x^7 \)[/tex]:
[tex]\[
182 x^7 (1 + x^3)
\][/tex]
However, examining our multiple-choice answers, we need to match the simplified expression with one of them directly. The closest match to our boxed expression, without factoring for a better match, is:
[tex]\[
182 x^7 + 182 x^{10}
\][/tex]
Therefore, the correct answer to the question is:
c. [tex]\( 182 x^7 + 182 x^{10} \)[/tex]
