Write the balanced equation for the decomposition of hydrogen peroxide to form water and oxygen.

Hydrogen peroxide is H2O2, while water is H2O and oxygen (a diatomic gas) is O2. The (unbalanced) reaction is:
H2O2 --> H2O + O2
Notice that the H2O2 has 2 H atoms, and so does H2. This means that both must have the same coefficients, and we can adjust the coefficient of O2. Since H2O2 has 2 O atoms, and H2O has 1, we multiply O2 by 1/2:
H2O2 --> H2O + (1/2)O2
This has an equivalent number of H and O atoms on either side, but we want the coefficients to be whole numbers, so we multiply everything by 2:
2H2O2 --> 2H2O + O2