The problem in the image asks to factor the expression $y^4 + xy$ completely.

Step-by-Step Solution:

1. Identify the common factor: Both terms in the expression, $y^4$ and $xy$, contain the variable $y$ as a factor.

2. Factor out the greatest common factor (GCF): The greatest common factor between $y^4$ and $xy$ is $y$. Factoring out $y$, we get: $y(y^3 + x)$

Thus, the factored form of $y^4 + xy$ is:

$\boxed{y(y^3 + x)}$

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. How do you factor expressions when the terms don't share any common variables?
2. Can you factor polynomials that include multiple variables?
3. How do you apply factoring when dealing with higher-degree polynomials?
4. What are some methods to check if your factorization is correct?
5. How does factoring help in solving algebraic equations?

Tip: Always check for common factors first before attempting more complex factoring methods.