square of sum

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

${(a+b)}^2=a^2+2ab+b^2.$ (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:

${(a+b+c)}^2=a^2+b^2+c^2+2bc+2ca+2ab$ (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

${(a+b+c+\mathrm{\dots })}^2=(a)a+(2a+b)b+(2a+2b+c)c+\mathrm{\dots }$ (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
Related topic	SquareRootOfPolynomial
Related topic	DifferenceOfSquares
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Related topic	ContraharmonicMeansAndPythagoreanHypotenuses
Related topic	CompletingTheSquare
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