Question

which polynomial expression represents a sum of cubes?
$(6 - s)(s^2 + 6s + 36)$
$(6 + s)(s^2 - 6s + 36)$
$(6 + s)(s^2 + 6s + 36)$
$(6 + s)(s^2 - 6s - 36)$

Explanation:

Step1: Recall sum of cubes formula

The formula for the sum of cubes is \(a^3 + b^3=(a + b)(a^2 - ab + b^2)\).

Step2: Identify \(a\) and \(b\)

Here, if we consider \(a = 6\) and \(b=s\), then \(a^3=6^3 = 216\) and \(b^3=s^3\). So \(a^3 + b^3=216 + s^3\).

Step3: Apply the formula

Using the sum of cubes formula \((a + b)(a^2 - ab + b^2)\) with \(a = 6\) and \(b = s\), we get \((6 + s)(6^2-6\times s + s^2)=(6 + s)(36-6s + s^2)=(6 + s)(s^2-6s + 36)\).

Answer:

\((6 + s)(s^2 - 6s + 36)\) (the second option)