square of sum

The well-known for squaring a sum of two numbers or is

(a+b)2=a2+2ab+b2. (1)

It may be derived by multiplying the binomial a+b by itself.

Similarly one can get the squaring for a sum of three summands:

(a+b+c)2=a2+b2+c2+2bc+2ca+2ab (2)

Its contents may be expressed as the

Rule.  The square of a sum is equal to the sum of the squares of all the summands plus the sum of all the double products of the summands in twos:


This is true for any number of summands.  The rule may be formulated also as

(a+b+c+)2=(a)a+(2a+b)b+(2a+2b+c)c+ (3)

which in the case of four summands is

(a+b+c+d)2=(a)a+(2a+b)b+(2a+2b+c)c+(2a+2b+2c+d)d. (4)

One can use the idea of (3) to find the , when one tries to arrange the polynomial into the form of the right hand side (http://planetmath.org/Equation) of (3).

Title square of sum
Canonical name SquareOfSum
Date of creation 2013-03-22 15:32:03
Last modified on 2013-03-22 15:32:03
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 9
Author pahio (2872)
Entry type Topic
Classification msc 30-00
Classification msc 26-00
Classification msc 11-00
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