To simplify the Boolean expression $x(x' + y)$, we can apply Boolean algebra rules and identities:

Step 1: Apply the Distributive Law:

$x(x' + y) = xx' + xy$

Step 2: Simplify using the Complement Law:

$xx' = 0$ This is because $x'$ is the complement of $x$, and $x \cdot x' = 0$.

Step 3: Simplify the expression:

$0 + xy = xy$

Final Simplified Expression:

$xy$

The simplified Boolean expression is $xy$.

Would you like further explanation or details?

Here are 5 related questions you can try:

1. Simplify the Boolean expression $(x + x')(y + y')$.
2. What is the simplified form of $(xy)' + x'$?
3. Use Boolean identities to simplify $(x + y)(x' + z)$.
4. How does the Distributive Law work in Boolean algebra?
5. What is the dual of the Boolean expression $xy + x'z$?

Tip: Always look for terms that can be eliminated using the complement or identity laws to simplify Boolean expressions quickly.