Factor the expression completely.
x, squared, y, cubed, minus, x, to the power 4 , y, to the power 4
x 
2
 y 
3
 −x 
4
 y 
4
 

To factor the given expression \( x^2y^3 - x^4y^4 \) completely, we can follow these steps:

1. **Factor out the greatest common factor (GCF):**
   - The GCF of the terms \( x^2y^3 \) and \( x^4y^4 \) is \( x^2y^3 \).
   - Factor out \( x^2y^3 \) from both terms.

   \[
   x^2y^3(x^0y^0 - x^{4-2}y^{4-3}) = x^2y^3(1 - x^2y)
   \]

2. **Check for further factorization:**
   - The expression inside the parentheses \( 1 - x^2y \) cannot be factored further using real numbers.

Thus, the completely factored form of the expression is:

\[
x^2y^3(1 - x^2y)
\]

Would you like further details or have any other questions?

Here are 5 related questions for practice:
1. Factor the expression \( 3x^3y^2 - 9x^2y^3 \).
2. Factor \( x^4 - y^4 \).
3. Find the GCF of \( 2x^5y^3 \) and \( 8x^3y^4 \).
4. Factor \( 4x^3y^2 - 16x^2y^3 + 8x^2y^2 \).
5. Simplify the expression \( (x^2 - y^2)(x^2 + y^2) \).

**Tip:** Always start by factoring out the greatest common factor (GCF) before attempting other methods like grouping or special products.

Factor the expression completely: x^2y^3 - x^4y^4

Discover how to completely factor the expression x^2y^3 - x^4y^4 by identifying and factoring out the greatest common factor (GCF). This problem is ideal for students in Grades 8-10 who are exploring algebraic concepts and factoring techniques.

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