You HAVE to Know How to USE this Formula - GRE and GMAT Math

a2 – b2 = (a + b)(a – b)

The difference of two squares comes up all the time, multiple times per GRE or GMAT test. Most students underestimate it badly.

It is virtually guaranteed to be in your exam. And it’s not enough just to agree with the formula, you know must know it forwards and backwards.

When I say backwards and forwards, I mean it is not just enough to recognise one of those two sides, say an expression such as (x + 4)(x – 4) and say ‘hey, that’s x2 – 42’. You must also recognise an expression such as 4x2 – y2 and know that it equals (2x + y)(2x – y).

If you don’t quite believe that (2x + y)(2x – y), for example, can equal something as simple as 4x2 – y2, try multiplying it out to show yourself how it works.

How is the difference of two squares formula tested?
Let’s do a couple of tough examples to get you ready for prime time GRE and GMAT Math.

(〖(x〗^4- x^2)〖(x〗^4+ x^2) )/(x^4+ x^2 ) – (〖(x〗^4- x^2)〖(x〗^4+ x^2) )/(x^4- x^2 )
= x^4- x^2 – (x^4+ x^2)
= x^4- x^2 – x^4- x^2
= -2x2

If p = (5)6 – (3)4, which of the following is the sum of the unique prime factors of p?
2
8
16
64
98

p = (53)2 – (32)2 = (53 + 32) (53 – 32)
(53 + 32) (53 – 32) = (134)(116)
(134)(116) = (2 x 67) (2 x 2 x 29)

After factorizing exponents, always calculate the value inside the brackets. This is:
(53 + 32)(53 – 32) = (134)(116).

Now, the question wants the sum of the prime factors of this answer, so we must prime factorize these numbers:
(134)(116) = (2x67)(2x2x29).

The three unique prime factors are 2, 29 and 67. The sum of these is 98.

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