To check the extensions on a purchase invoice means to verify that the number of units of each item multiplied by its unit cost agrees with the total dollar amount for each item. For example, if 15 units of Item Q have a per unit cost of $5, the total cost for Item Q should be $75.
To foot the invoice means to add up the extended costs and verify the total with the amount appearing as the total on the invoice. For example, if the invoice has extended costs of $75 for Item Q and $210 for Item Z, the invoice total should be $285.