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Homedifference of squares

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# difference of squares

One of the most known and used formulas of mathematics is the one concerning the product of sum and difference:

$\displaystyle(a+b)(a-b)=a^{2}-b^{2}$ | (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

$\displaystyle a^{2}-b^{2}=(a+b)(a-b)$ | (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.

## Mathematics Subject Classification

97D99*no label found*26C99

*no label found*13A99

*no label found*

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