Question

use the distributive property to remove the parentheses.
$2z^{3}\left(10 - 8z^{2}\
ight)$
simplify your answer as much as possible.

Explanation:

Step1: Apply distributive property

The distributive property states that \( a(b - c)=ab - ac \). Here, \( a = 2z^{3} \), \( b = 10 \), and \( c = 8z^{2} \). So we distribute \( 2z^{3} \) to both terms inside the parentheses:
\( 2z^{3}\times10-2z^{3}\times8z^{2} \)

Step2: Simplify each term

For the first term: \( 2z^{3}\times10 = 20z^{3} \)
For the second term: When multiplying variables with exponents, we use the rule \( a^{m}\times a^{n}=a^{m + n} \). So \( 2z^{3}\times8z^{2}=(2\times8)z^{3 + 2}=16z^{5} \)
Putting it together, we get \( 20z^{3}-16z^{5} \)

Answer:

\( 20z^{3}-16z^{5} \)