Factor the expression completely.
x, to the power 4 , y, minus, x, to the power 5 , y, to the power 5
x 
4
 y−x 
5
 y 
5

We are asked to factor the expression:

\[
x^4y - x^5y^5
\]

### Step 1: Identify common factors
The common factors between the two terms are \(x^4\) and \(y\), so we can factor them out:

\[
x^4y(x^0 - xy^4)
\]

Since \(x^0 = 1\), we simplify the expression inside the parentheses:

\[
x^4y(1 - xy^4)
\]

### Final Factored Form:
\[
x^4y(1 - xy^4)
\]

This is the fully factored form of the given expression.

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Would you like further details on factoring? Here are some related questions you could explore:

1. How can you factor more complex polynomials?
2. What are the rules for factoring when dealing with multiple variables?
3. How does the distributive property help in factoring?
4. What is the significance of common factors in polynomial expressions?
5. How would the factoring change if exponents were higher or more terms were involved?

**Tip:** Always look for the greatest common factor (GCF) first when factoring any expression!

Factor the expression completely. x^4y - x^5y^5

This page explains how to factor the polynomial expression x^4y - x^5y^5 step-by-step. Learn key concepts such as the distributive property and identifying common factors. Suitable for students in Grades 9-12.

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