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.

Learn how to factorize the expression a^5 - 4ab^4 with a detailed step-by-step solution. This problem involves algebraic concepts such as polynomials, factoring, and the difference of squares formula. Suitable for high school students.

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