Question

use the distributive property to remove the parentheses.
\\((6b^3 - 3b^5 + 5)10b^2\\)
simplify your answer as much as possible.

Explanation:

Step1: Apply distributive property

Multiply each term inside the parentheses by \(10b^2\). So we have:
\(6b^3 \times 10b^2 - 3b^5 \times 10b^2 + 5 \times 10b^2\)

Step2: Simplify each term

For the first term: \(6\times10 = 60\), and using the rule \(a^m\times a^n=a^{m + n}\), \(b^3\times b^2=b^{3+2}=b^5\), so the first term is \(60b^5\).
For the second term: \(- 3\times10=-30\), \(b^5\times b^2 = b^{5 + 2}=b^7\), so the second term is \(-30b^7\).
For the third term: \(5\times10 = 50\), so the third term is \(50b^2\).

Combining these terms, we get \(60b^5-30b^7 + 50b^2\) (we can also re - order the terms by degree: \(-30b^7+60b^5 + 50b^2\)).

Answer:

\(-30b^{7}+60b^{5}+50b^{2}\)