To determine if the expression can be factored as a sum or difference of cubes, let’s analyze it step by step.
Step 1: Identify the Expression
The expression is:
Step 2: Factor Out the GCF
Before checking for sums of cubes, we should look for a Greatest Common Factor (GCF).
The GCF of the terms and (250) is (2). We can factor this out:
Step 3: Recognize the Form
Now we have:
Next, we can recognize that can be expressed as a sum of cubes because:
So we rewrite it as: