1. **State the problem:** Construct circuits for the Boolean expression $xyz + xyz$. 2. **Understand the expression:** The expression is $xyz + xyz$. Notice that $xyz$ and $xyz$ differ only in the variable $z$ and its complement $z$. 3. **Apply Boolean algebra rules:** Use the Distributive Law: $$xyz + xyz = xy(z + z)$$ 4. **Simplify using the Complement Law:** Since $z + z = 1$, $$xy(z + z) = xy \cdot 1 = xy$$ 5. **Final simplified expression:** The circuit can be constructed for $xy$ only. 6. **Circuit construction:** - Use an AND gate with inputs $x$ and $y$. - The output of this AND gate is the output of the entire expression. This simplification reduces the complexity of the circuit significantly.