# 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:

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

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