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.
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.
