How do I evaluate something like 3070^2-3069^2?

This looks pretty daunting, but the key to this sort of a problem, which has come up a couple of times in previous PAT tests, is to recognise that this expression is actually the difference of two squares. It can be generalised to the problem of evaluating:

x2-y2

which has as its solution:

x2-y2 = (x+y)(x-y)

so in this case:

30702-30692 = (3070+3069)(3070-3069)=(6139)(1)=6139

SC
Answered by Sam C. PAT tutor

2829 Views

See similar PAT University tutors

Related PAT University answers

All answers ▸

Given that during a total solar eclipse the Sun is fully hidden by the Moon, calculate the radius of the Moon. (You may use the following: Solar radius 700,000 km, Sun-Earth distance 150,000,000 km, Moon-Earth distance 400,000 km)


a boat is in a still lake with its anchor up in the boat, it then drops its anchor till it hits the bottom of the lake. Is the water level highest a) when the anchor is in the water. b) when the anchor is in the boat. c) it makes no difference.


Five point charges, each of positive charge q, are arranged to form the corners of a uniform pentagon. A point charge Q is placed at the pentagon's centre. One of the corner charges is removed. What force does the centre charge experience?


How are you to find 2007^2 − 2006^2 without a calculator?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences