Question

use the distributive property to remove the parentheses.
$9z^{2}\left(2 - 6z^{5}\
ight)$
simplify your answer as much as possible.

Explanation:

Step1: Apply distributive property

The distributive property states that \(a(b - c)=ab - ac\). Here, \(a = 9z^{2}\), \(b = 2\), and \(c = 6z^{5}\). So we have:
\(9z^{2}\times2-9z^{2}\times6z^{5}\)

Step2: Simplify each term

For the first term: \(9z^{2}\times2 = 18z^{2}\)
For the second term, use the rule of exponents \(a^{m}\times a^{n}=a^{m + n}\). So \(9z^{2}\times6z^{5}=(9\times6)z^{2 + 5}=54z^{7}\)
Putting it together, we get \(18z^{2}-54z^{7}\)

Answer:

\(18z^{2}-54z^{7}\)