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:


which has as its solution:

x2-y2 = (x+y)(x-y)

so in this case:

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

Sam C. A Level Physics tutor, GCSE Physics tutor, A Level Maths tutor...

6 months ago

Answered by Sam, an Uni Admissions Test .PAT. tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


£30 /hr

Henri F.

Degree: Aerospace Engineering MEng (Masters) - Bristol University

Subjects offered: .PAT., Physics+ 4 more

Further Mathematics

“About Me I am an Aerospace Engineer currently studying my MEng at the University of Bristol. I have always been fascinated with space, spacecraft and satellites. I intend on going on to complete a PhD specialising inSpacecraft Control...”

£25 /hr

Tom C.

Degree: Engineering Science (Masters) - Oxford, Jesus College University

Subjects offered: .PAT., Physics+ 3 more

Further Mathematics
-Oxbridge Preparation-

“About me I’m Tom, I’m a third year Engineer at Oxford University. I’m very patient and friendly and I’ve always had love for how things are put together, this has gone onto the science behind it. In our lessons I want to show you what...”

About the author

Sam C.

Currently unavailable: for new students

Degree: MEng Engineering Science (Masters) - Oxford, New College University

Subjects offered: .PAT., Physics+ 2 more

Further Mathematics

“ABOUT ME:I am studying Engineering Science at New College, Oxford. I am also a key member of the prestigious University Boat Club, coxing the Oxford Blue boat in the 2016 Boat Race. I am passionate about academic success and about Ma...”

You may also like...

Posts by Sam

A capacitor discharge circuit of time constant 45ms includes a capacitor and resistor. The capacitor has a capacitance of 18µF What is the resistance of the resistor?

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

Other Uni Admissions Test .PAT. questions

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

What is the sum of the series 2/3 − 2/9 + 2/27 − ....? (PAT Q1 2013)

How do I approximate an irrational square root without using a calculator?

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

View Uni Admissions Test .PAT. tutors


We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss