Step 1: Think of the economy's circular flow of income:
Whatever is produced generates an equal amount of income for factors of production, which is then spent by households/government/firms — production, income, and expenditure are three views of the same flow.
Step 2: Write the formula matching each view:
Production view: sum of value added at each stage (avoids double counting intermediate goods). Income view: sum of factor payments (wages+rent+interest+profit) plus depreciation and net indirect taxes. Expenditure view: sum of final spending, C+I+G+(X-M).
Step 3: Note why all three must match:
Since one firm's output value becomes another's income, which becomes someone's expenditure, in a closed accounting system the three totals are identically equal — this identity is the basis for cross-checking national income estimates.
Final Answer:
Production method (sum of value added), Income method (sum of factor incomes + depreciation + net indirect taxes), and Expenditure method (C+I+G+X-M) are the three GDP identities.