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difference of squares
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One of the most known and used formulas of mathematics is the one concerning the product of sum and difference:
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(1) |
This form may be used for multiplying any sum of two numbers (terms) by the difference of the same numbers (terms).
In the form
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(2) |
the formula is used for factoring binomials which are the difference of two squares.
(1) is sometimes called the conjugate rule, especially in articles written in Sweden (in Swedish: konjugatregel).
(1) is an identic equation for all numbers $a,\,b$ and, more generally, for arbitrary elements $a,\,b$ of any commutative ring. Conversely, it is easy to justify that if (1) is true for all elements $a,\,b$ of a ring, then the ring is commutative. By the way, $a\!+\!b$ and $a\!-\!b$ also commute with each other in a non-commutative ring.
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"difference of squares" is owned by pahio. [ full author list (2) ]
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Cross-references: non-commutative, commutative, ring, conversely, commutative ring, identic equation, squares, binomials, numbers, difference, sum, product
There are 2 references to this entry.
This is version 7 of difference of squares, born on 2008-01-20, modified 2008-03-27.
Object id is 10204, canonical name is DifferenceOfSquares.
Accessed 2523 times total.
Classification:
| AMS MSC: | 13A99 (Commutative rings and algebras :: General commutative ring theory :: Miscellaneous) | | | 26C99 (Real functions :: Polynomials, rational functions :: Miscellaneous) | | | 97D99 (Mathematics education :: Education and instruction in mathematics :: Miscellaneous) |
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