Question

125k³ - b³

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, we can rewrite \(125k^3\) as \((5k)^3\) since \(5^3 = 125\) and \((k)^3=k^3\). So now our expression is \((5k)^3 - b^3\).

Step2: Apply the difference of cubes formula

Using the formula \(a^3 - b^3=(a - b)(a^2+ab + b^2)\) where \(a = 5k\) and \(b=b\), we substitute these values into the formula.

First, find \(a - b\): \(5k - b\).

Then, find \(a^2+ab + b^2\): \((5k)^2+(5k)(b)+b^2 = 25k^2+5kb + b^2\).

So, \((5k)^3 - b^3=(5k - b)(25k^2+5kb + b^2)\).

Answer:

\((5k - b)(25k^2 + 5kb + b^2)\)