the telephone company wants to add an area code composed of 2 letters to every phone number . in order to do so , the company chose a special sign language containing 424 different signs . if the company used 422 of the signs fully and two remained unused , how many additional area codes can be created if the company uses all 424 signs ?
"# of 2 - letter codes possible from 424 different signs = 424 * 424 . # of 2 - letter codes possible from 422 different signs = 422 * 422 . the difference = 424 ^ 2 - 422 ^ 2 = ( 424 - 422 ) ( 424 + 422 ) = 1692 . answer : c ."
multiply(multiply(422, subtract(424, 422)), subtract(424, 422))