The expression you've provided is:

$a^5 - 4ab^4$

This expression can be factored. Let's factor it:

$a^5 - 4ab^4 = a(a^4 - 4b^4)$

Next, we can factor $a^4 - 4b^4$ further using the difference of squares formula:

$a^4 - 4b^4 = (a^2)^2 - (2b^2)^2$

$= (a^2 - 2b^2)(a^2 + 2b^2)$

So, the fully factored form of the original expression is:

$a^5 - 4ab^4 = a(a^2 - 2b^2)(a^2 + 2b^2)$

Would you like further details or have any questions?

Here are 5 related questions to consider:

1. How would you factor $a^5 - 5ab^4$?
2. Can you factor $a^6 - b^6$ using a similar method?
3. How do you factor expressions involving the sum of cubes, such as $a^3 + b^3$?
4. What is the general formula for factoring the difference of squares?
5. How would you expand $(a^2 - 2b^2)(a^2 + 2b^2)$ back to its original form?

Tip: Always look for common factors first before applying other factoring techniques.