Balance the chemical equation Al₂O₃ → Al + O₂.

We are given the chemical equation:

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

This represents the decomposition of aluminum oxide into aluminum metal and oxygen gas. Our task is to balance this chemical equation.

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Step 1: Understand the unbalanced equation

On the left:
- 2 Al atoms (in Al₂O₃)
- 3 O atoms (in Al₂O₃)

On the right:
- 1 Al atom (in Al)
- 2 O atoms (in O₂, since it's a diatomic molecule)

So the atoms are not balanced.

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Step 2: Balance the atoms

Let’s balance one element at a time.

#### Start with oxygen:
- Left: 3 O atoms in Al₂O₃
- Right: O₂ has 2 O atoms per molecule

We need to make the number of oxygen atoms even on both sides. The least common multiple of 3 and 2 is 6.

So we want 6 oxygen atoms on each side.

To get 6 O atoms on the left:
- Multiply Al₂O₃ by 2:
$$
2\text{Al}_2\text{O}_3 \rightarrow \text{?}
$$
Now we have:
- 4 Al atoms (since 2 × 2 = 4)
- 6 O atoms (since 2 × 3 = 6)

To get 6 O atoms on the right:
- O₂ has 2 O atoms per molecule → so we need 3 O₂ molecules:
$$
\text{O}_2 \times 3 = 3\text{O}_2
$$

Now we have:
$$
2\text{Al}_2\text{O}_3 \rightarrow \text{Al} + 3\text{O}_2
$$

But now check aluminum:
- Left: 4 Al atoms (from 2 Al₂O₃)
- Right: only 1 Al atom

So we need 4 Al atoms on the right → put 4 Al.

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Final balanced equation:

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

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Check atom balance:

| Atom | Left Side | Right Side |
|------|-----------|------------|
| Al | 2 × 2 = 4 | 4 |
| O | 2 × 3 = 6 | 3 × 2 = 6 |

✔ Balanced!

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Answer:

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

This is the balanced chemical equation.