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From: Internet Comment Copy link September 3

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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

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:

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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 :

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

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

**Whoa, Dude... It worked!**

**Here's another one:**

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