Balance the chemical equation Al₂O₃ → Al + O₂.

To balance the chemical equation provided:

$$
\text{Al}_2\text{O}_3 \rightarrow \text{Al} + \text{O}_2
$$

Step-by-Step Solution:

1. Identify the reactants and products:
- Reactant: $\text{Al}_2\text{O}_3$ (aluminum oxide)
- Products: $\text{Al}$ (aluminum) and $\text{O}_2$ (oxygen gas)

2. Count the number of atoms of each element on both sides of the equation:

- Left side (Reactants):
- Aluminum (Al): 2 atoms (from $\text{Al}_2\text{O}_3$)
- Oxygen (O): 3 atoms (from $\text{Al}_2\text{O}_3$)

- Right side (Products):
- Aluminum (Al): 1 atom (from $\text{Al}$)
- Oxygen (O): 2 atoms (from $\text{O}_2$)

3. Balance the aluminum (Al) atoms:
- There are 2 Al atoms on the left side but only 1 Al atom on the right side.
- To balance Al, we need to add a coefficient of 2 in front of $\text{Al}$ on the right side:
$$
\text{Al}_2\text{O}_3 \rightarrow 2\text{Al} + \text{O}_2
$$

4. Balance the oxygen (O) atoms:
- After adding the coefficient for Al, the equation is:
$$
\text{Al}_2\text{O}_3 \rightarrow 2\text{Al} + \text{O}_2
$$
- Now, count the O atoms again:
- Left side: 3 O atoms (from $\text{Al}_2\text{O}_3$)
- Right side: 2 O atoms (from $\text{O}_2$)
- To balance the O atoms, we need to adjust the coefficient of $\text{O}_2$. Since there are 3 O atoms on the left and 2 O atoms per molecule of $\text{O}_2$, we need $\frac{3}{2}$ molecules of $\text{O}_2$. However, coefficients in balanced equations must be whole numbers. Therefore, multiply the entire equation by 2 to eliminate the fraction:
$$
2 \times (\text{Al}_2\text{O}_3 \rightarrow 2\text{Al} + \text{O}_2)
$$

5. Multiply through by 2:
- Reactants: $2 \times \text{Al}_2\text{O}_3 = 2\text{Al}_2\text{O}_3$
- Products: $2 \times 2\text{Al} = 4\text{Al}$ and $2 \times \text{O}_2 = 2\text{O}_2$

The balanced equation becomes:
$$
2\text{Al}_2\text{O}_3 \rightarrow 4\text{Al} + 3\text{O}_2
$$

6. Verify the balanced equation:
- Left side (Reactants):
- Aluminum (Al): $2 \times 2 = 4$ atoms
- Oxygen (O): $2 \times 3 = 6$ atoms
- Right side (Products):
- Aluminum (Al): 4 atoms
- Oxygen (O): $3 \times 2 = 6$ atoms

Both sides have the same number of atoms for each element, so the equation is balanced.

Final Answer:

$$
\boxed{2\text{Al}_2\text{O}_3 \rightarrow 4\text{Al} + 3\text{O}_2}
$$