Question

question
factor completely:
$a^3 - s^9$
answer attempt 1 out of 2

Explanation:

Step1: Recognize the difference of cubes

The expression \(a^3 - s^9\) can be written as \(a^3 - (s^3)^3\), which is a difference of cubes. The formula for factoring a difference of cubes is \(x^3 - y^3=(x - y)(x^2+xy + y^2)\). Here, \(x = a\) and \(y = s^3\).

Step2: Apply the difference of cubes formula

Substitute \(x = a\) and \(y = s^3\) into the formula:
\(a^3-(s^3)^3=(a - s^3)(a^2+a\times s^3+(s^3)^2)\)
Simplify the second factor: \((s^3)^2 = s^{6}\), so the expression becomes \((a - s^3)(a^2 + a s^3 + s^6)\)

Answer:

\((a - s^3)(a^2 + a s^3 + s^6)\)