Question

use the distributive property to remove the parentheses.
10b³(8 - 3b⁵)
simplify your answer as much as possible.

Explanation:

Step1: Apply distributive property

The distributive property states that \( a(b - c)=ab - ac \). Here, \( a = 10b^{3} \), \( b = 8 \), and \( c = 3b^{5} \). So we multiply \( 10b^{3} \) with each term inside the parentheses:
\( 10b^{3}\times8-10b^{3}\times3b^{5} \)

Step2: Simplify each term

For the first term: \( 10b^{3}\times8 = 80b^{3} \)
For the second term, use the rule of exponents \( a^{m}\times a^{n}=a^{m + n} \). So \( 10b^{3}\times3b^{5}=(10\times3)b^{3 + 5}=30b^{8} \)
Putting it together, we get \( 80b^{3}-30b^{8} \)

Answer:

\( 80b^{3}-30b^{8} \)