# 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:

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

 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