Question

use the distributive property to remove the parentheses.
$left(6z^{4} - 8z^{5}
ight)3z^{3}$
simplify your answer as much as possible.

Explanation:

Step1: Apply distributive property

Multiply each term inside the parentheses by \(3z^3\).
\((6z^4 - 8z^5) \cdot 3z^3 = 6z^4 \cdot 3z^3 - 8z^5 \cdot 3z^3\)

Step2: Multiply coefficients and add exponents (product rule)

For \(6z^4 \cdot 3z^3\): Multiply coefficients \(6 \cdot 3 = 18\), add exponents \(z^{4 + 3} = z^7\), so it becomes \(18z^7\).
For \(-8z^5 \cdot 3z^3\): Multiply coefficients \(-8 \cdot 3 = -24\), add exponents \(z^{5 + 3} = z^8\), so it becomes \(-24z^8\).

Answer:

\(18z^7 - 24z^8\)