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# Sum of Squares Rule

### Sum of Squares Function -- from Wolfram MathWorld

Sum of Squares Function

The number of representations of
by
squares, allowing zeros and distinguishing signs and order, is denoted
. The special case
corresponding to two squares is often denoted simply
(e.g., Hardy and Wright 1979, p. 241; Shanks 1993, p. 162).

For example, consider the number of ways of representing 5 as the sum of two squares:

### How to Factor the Difference of Two Perfect Squares

How to Factor the Difference of Two Perfect Squares

How to Factor the Difference of Two Perfect Squares

If two terms in a binomial are perfect squares separated by subtraction, then you can factor them. To factor the difference of two perfect squares, remember this rule: if subtraction separates two squared terms, then the sum and the difference of the two square roots factor the binomial. For example:

THE ALGEBRA OF SUMMATION NOTATION

The following problems involve the algebra (manipulation) of summation notation. Summation notation is used to define the definite integral of a continuous function of one variable on a closed interval. Let's first briefly define summation notation. If f(i) represents some expression (function) involving i, then
has the following meaning :

### Factoring the Sum of Two Squares 2 | Coolmath.com

Does it work? Let's check it using FOIL!

You treat the i guys just like regular variables... adding "like terms" etc.

And we know that

Whoa, Dude... It worked!

Here's another one:

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