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单词 SquareOfSum
释义

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:

(iai)2=iai2+2i<jaiaj.

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).

Titlesquare of sum
Canonical nameSquareOfSum
Date of creation2013-03-22 15:32:03
Last modified on2013-03-22 15:32:03
Ownerpahio (2872)
Last modified bypahio (2872)
Numerical id9
Authorpahio (2872)
Entry typeTopic
Classificationmsc 30-00
Classificationmsc 26-00
Classificationmsc 11-00
Related topicSquareRootOfPolynomial
Related topicDifferenceOfSquares
Related topicHeronianMeanIsBetweenGeometricAndArithmeticMean
Related topicContraharmonicMeansAndPythagoreanHypotenuses
Related topicCompletingTheSquare
Related topicTriangleInequalityOfComplexNumbers
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更新时间:2025/5/4 11:55:08