Question

question
factor $125 - 27b^3$ completely.
answer attempt 1 out of 2

Explanation:

Step1: Identify the formula for difference of cubes

The difference of cubes formula is \(a^3 - b^3=(a - b)(a^2+ab + b^2)\). Here, \(125 = 5^3\) and \(27b^3=(3b)^3\), so \(a = 5\) and \(b = 3b\).

Step2: Apply the difference of cubes formula

Substitute \(a = 5\) and \(b = 3b\) into the formula \(a^3 - b^3=(a - b)(a^2+ab + b^2)\):
\[

$$\begin{align*} 5^3-(3b)^3&=(5 - 3b)(5^2+5\times(3b)+(3b)^2)\\ &=(5 - 3b)(25 + 15b+9b^2) \end{align*}$$

\]

Answer:

\((5 - 3b)(25 + 15b + 9b^2)\)