To factor the expression 16x^5 - x^3 completely, we can factor out the greatest common factor (GCF) and then look for any additional factors.
Step 1: Factor out the GCF.
The GCF of 16x^5 and -x^3 is x^3. By factoring out x^3, we have:
x^3(16x^2 - 1)
Step 2: Look for additional factors.
Now, we need to examine the expression (16x^2 - 1) to see if it can be factored further. This expression represents the difference of squares, which can be factored as follows:
16x^2 - 1 = (4x)^2 - 1^2
= (4x - 1)(4x + 1)
Therefore, the completely factored form of 16x^5 - x^3 is:
x^3(4x - 1)(4x + 1)
I hope this helps! ;)