Question

use the distributive property to remove the parentheses.\\(3b^{6}(10b^{7}+8b)\\)\
simplify your answer as much as possible.

Explanation:

Step1: Apply distributive property

Multiply \(3b^6\) with each term inside the parentheses: \(3b^6 \times 10b^7 + 3b^6 \times 8b\)

Step2: Simplify each product

For the first term: \(3\times10 = 30\), and using the rule \(a^m \times a^n = a^{m + n}\), \(b^6 \times b^7 = b^{6 + 7}=b^{13}\), so first term is \(30b^{13}\). For the second term: \(3\times8 = 24\), \(b^6 \times b = b^{6+1}=b^7\), so second term is \(24b^7\). Combine them: \(30b^{13}+24b^7\)

Answer:

\(30b^{13} + 24b^7\)