The standard accounting equation shows how the various types of accounts listed in a company's chart of accounts balance each other, and is stated as follows:
Assets = Liabilities + Shareholders' Equity
The assets in the standard accounting equation are the resources that a company has available for its use, such as cash, accounts receivable, fixed assets, and inventory.
The company pays for these resources by either incurring liabilities (which is the Liabilities part of the accounting equation) or by obtaining funding from investors or through the accumulation of retained earnings over time (which is the Shareholders' Equity part of of the equation). Thus, you have resources with offsetting claims against those resources, either from creditors or investors. All three components of the accounting equation appear in the balance sheet, which reveals the financial position of a business as of the date stated on the document.
The expanded accounting equation reveals all of the components of the shareholders' equity part of the accounting equation. The expanded equation is:
Assets = Liabilities + (Paid in Capital - Dividends - Treasury Stock + Revenue - Expenses)
This additional level of detail shows how profits and losses from the income statement appear in the shareholders' equity section of the balance sheet, as well as how cash outflows to pay for dividends and the repurchase of stock will reduce the amount of shareholders' equity.
The components of the expanded accounting equation are somewhat different for a sole proprietorship, where the components of the shareholders' equity part of the equation are replaced by the owner's capital and owner's draws accounts.
The concept of the expanded accounting equation does not extend to the asset and liability sides of the accounting equation, since those elements are not directly altered by changes in the income statement. Thus, there is no need to show additional detail for the asset or liability sides of the accounting equation.