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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 $a\!+\!b$ 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: $$\left(\sum_ia_i\right)^2 \;=\; \sum_ia_i^2+2\!\sum_{i \neq j}a_ia_j.$$
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, numbers, sum
There are 2 references to this entry.
This is version 5 of square of sum, born on 2005-10-09, modified 2009-01-01.
Object id is 7427, canonical name is SquareOfSum.
Accessed 16333 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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