Question

use the distributive property to remove the parentheses. 3b⁶(2b⁸ + 10b + 2) simplify your answer as much as possible.

Explanation:

Step1: Apply distributive property

Multiply \(3b^6\) with each term inside the parentheses:
\(3b^6 \cdot 2b^8 + 3b^6 \cdot 10b + 3b^6 \cdot 2\)

Step2: Simplify each term

• For \(3b^6 \cdot 2b^8\): Multiply coefficients (\(3 \cdot 2 = 6\)) and add exponents of \(b\) (\(b^6 \cdot b^8 = b^{6 + 8} = b^{14}\)), so \(6b^{14}\).
• For \(3b^6 \cdot 10b\): Multiply coefficients (\(3 \cdot 10 = 30\)) and add exponents of \(b\) (\(b^6 \cdot b = b^{6 + 1} = b^7\)), so \(30b^7\).
• For \(3b^6 \cdot 2\): Multiply coefficients (\(3 \cdot 2 = 6\)), so \(6b^6\).

Answer:

\(6b^{14} + 30b^7 + 6b^6\)