Question

use the distributive property to remove the parentheses.
$5x^6(3x + 10x^5)$
simplify your answer as much as possible.

Explanation:

Step1: Apply distributive property

Multiply \(5x^6\) with each term inside the parentheses: \(5x^6 \cdot 3x + 5x^6 \cdot 10x^5\)

Step2: Simplify each term

For the first term: \(5 \cdot 3 \cdot x^6 \cdot x = 15x^{6 + 1} = 15x^7\) (using \(a^m \cdot a^n = a^{m + n}\))
For the second term: \(5 \cdot 10 \cdot x^6 \cdot x^5 = 50x^{6 + 5} = 50x^{11}\)
Combine the simplified terms.

Answer:

\(15x^7 + 50x^{11}\)