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square of sum
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(Topic)
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The well-known formula for squaring a sum of two numbers or terms is
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(1) |
It may be derived by multiplying the binomial  by itself.
Similarly one can get the squaring formula for a sum of three summands:
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(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
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(3) |
which in the case of four summands is
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(4) |
One can use the idea of (3) to find the square root of a polynomial, when one tries to arrange the polynomial into the form of the right hand side of (3).
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"square of sum" is owned by pahio.
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Cross-references: right, polynomial, products, plus, square, binomial, sum
There are 2 references to this entry.
This is version 4 of square of sum, born on 2005-10-09, modified 2005-12-13.
Object id is 7427, canonical name is SquareOfSum.
Accessed 7704 times total.
Classification:
| AMS MSC: | 26-00 (Real functions :: General reference works ) | | | 30-00 (Functions of a complex variable :: General reference works ) | | | 11-00 (Number theory :: General reference works ) |
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Pending Errata and Addenda
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