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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 :

To simplify the expression [tex]\(14 x^5(13 x^2+13 x^5)\)[/tex], we will distribute the term outside the parentheses by multiplying it with each term inside the parentheses.

1. Start with the expression:
[tex]\[
14 x^5(13 x^2 + 13 x^5)
\][/tex]

2. Distribute the [tex]\(14 x^5\)[/tex] to each term inside the parentheses:

- Multiply [tex]\(14 x^5\)[/tex] by [tex]\(13 x^2\)[/tex]:
[tex]\[
14 \cdot 13 \cdot x^5 \cdot x^2 = 182 x^{5+2} = 182 x^7
\][/tex]

- Multiply [tex]\(14 x^5\)[/tex] by [tex]\(13 x^5\)[/tex]:
[tex]\[
14 \cdot 13 \cdot x^5 \cdot x^5 = 182 x^{5+5} = 182 x^{10}
\][/tex]

3. Combine these results to obtain the simplified expression:
[tex]\[
182 x^7 + 182 x^{10}
\][/tex]

Thus, the simplified form of the expression is [tex]\(182 x^7 + 182 x^{10}\)[/tex], which corresponds to option c.