Expenditure method estimates expenditure on domestic product, i.e. expenditure on final goods and services produced within the economic territory of the country. It includes expenditure by residents and non residents both. Exports though purchased by non residents are produced within the economic territory and are therefore a part of domestic product.
Domestic product can be greater than national product, if the factor income paid to the rest of the world is greater than the factor income received from the rest of the world, i.e., when net factor income received from abroad is negative.