Question

use the distributive property to remove the parent
$5c^{3}\left(6c^{8} + 3c + 7\
ight)$
simplify your answer as much as possible.

Explanation:

Step1: Apply distributive property

Multiply \(5c^3\) with each term inside the parentheses:
\(5c^3 \times 6c^8 + 5c^3 \times 3c + 5c^3 \times 7\)

Step2: Simplify each term

For the first term: \(5\times6 = 30\), and using the rule \(a^m\times a^n=a^{m + n}\), \(c^3\times c^8=c^{3 + 8}=c^{11}\), so the first term is \(30c^{11}\).
For the second term: \(5\times3 = 15\), and \(c^3\times c=c^{3+1}=c^4\), so the second term is \(15c^4\).
For the third term: \(5\times7 = 35\), and we have \(35c^3\).

Answer:

\(30c^{11}+15c^4 + 35c^3\)