Question

use the distributive property to remove the parentheses.
$left(2x^{4}-8x^{5}+3
ight)3x^{2}$
simplify your answer as much as possible.

Explanation:

Step1: Distribute \(3x^2\) to each term

Multiply \(3x^2\) with \(2x^4\), \(-8x^5\), and \(3\) respectively.
For \(2x^4 \times 3x^2\): Using the rule \(a^m \times a^n = a^{m + n}\), we get \(2\times3\times x^{4 + 2}=6x^6\).
For \(-8x^5 \times 3x^2\): Similarly, \(-8\times3\times x^{5 + 2}=-24x^7\).
For \(3\times3x^2\): We get \(9x^2\).

Step2: Combine the terms

After distribution, we have \(6x^6 - 24x^7 + 9x^2\). We can reorder the terms by degree (from highest to lowest) to get \(-24x^7 + 6x^6 + 9x^2\).

Answer:

\(-24x^7 + 6x^6 + 9x^2\)