Question

use the distributive property to remove the parentheses.
$(5b^3 - 6b^4)2b^5$
simplify your answer as much as possible.

Explanation:

Step1: Apply distributive property

The distributive property states that \( (a - b)c = ac - bc \). So we distribute \( 2b^5 \) to both terms inside the parentheses:
\( (5b^3 - 6b^4)2b^5 = 5b^3 \cdot 2b^5 - 6b^4 \cdot 2b^5 \)

Step2: Multiply coefficients and use exponent rule

For the first term: Multiply the coefficients \( 5 \) and \( 2 \), and use the exponent rule \( a^m \cdot a^n = a^{m + n} \) for the variables.
\( 5b^3 \cdot 2b^5=(5\times2)b^{3 + 5}=10b^8 \)
For the second term: Multiply the coefficients \( - 6 \) and \( 2 \), and use the exponent rule for the variables.
\( -6b^4 \cdot 2b^5=(-6\times2)b^{4+5}=-12b^9 \)

Step3: Combine the terms

Putting the two terms together, we get:
\( 10b^8-12b^9 \)

Answer:

\( 10b^8 - 12b^9 \)