difference of squares

One of the most known and used formulas (http://planetmath.org/Equation) of mathematics is the one concerning the product of sum and difference:

(a+b)(a-b)=a2-b2 (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

a2-b2=(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 commutativePlanetmathPlanetmathPlanetmath.  By the way, a+b and a-b also commute with each other in a non-commutative ring.

Title difference of squares
Canonical name DifferenceOfSquares
Date of creation 2013-03-22 17:45:11
Last modified on 2013-03-22 17:45:11
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 10
Author pahio (2872)
Entry type Topic
Classification msc 97D99
Classification msc 26C99
Classification msc 13A99
Synonym conjugate rule
Related topic ConjugationMnemonic
Related topic ExampleOnSolvingAFunctionalEquation
Related topic SquareOfSum
Related topic GroupingMethodForFactorizingPolynomials
Related topic IncircleRadiusDeterminedByPythagoreanTriple
Related topic FactoringASumOrDifferenceOfTwoCubes
Related topic Polynomial
Related topic SineOfAngleOfTriangle
Related topic RepresentantsOfQuadraticRe