Let's factor the expression \( a^5 - 4ab^4 \).

Given expression:
\[ a^5 - 4ab^4 \]

Step 1: Factor out the greatest common factor (GCF).

The GCF of the terms \( a^5 \) and \( 4ab^4 \) is \( a \). So, factor \( a \) out:

\[ a(a^4 - 4b^4) \]

Step 2: Notice that \( a^4 - 4b^4 \) is a difference of squares.

The difference of squares can be factored as:
\[ a^4 - 4b^4 = (a^2 - 2b^2)(a^2 + 2b^2) \]

Step 3: Substitute this back into the factored expression:

\[ a^5 - 4ab^4 = a(a^2 - 2b^2)(a^2 + 2b^2) \]

So the fully factored form of \( a^5 - 4ab^4 \) is:

\[ \boxed{a(a^2 - 2b^2)(a^2 + 2b^2)} \]

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. How would you factor the expression \( a^6 - b^6 \)?
2. What would be the factorization of \( a^4 - 16b^4 \)?
3. Can you apply the difference of squares method to factor \( x^4 - 16 \)?
4. How do you recognize and factor a perfect square trinomial?
5. What happens when you try to factor \( a^5 + 4ab^4 \)?

**Tip:** When dealing with polynomial expressions, always start by factoring out the greatest common factor (GCF) before looking for other factorization methods.

Learn how to factorize the expression a^5 - 4ab^4 using polynomial factorization techniques. This problem involves the difference of squares method and is suitable for advanced high school students and beyond.

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