# square of sum

The well-known for squaring a sum of two numbers or is

${(a+b)}^{2}={a}^{2}+2ab+{b}^{2}.$ | (1) |

It may be derived by multiplying the binomial $a+b$ by itself.

Similarly one can get the squaring for a sum of three summands:

${(a+b+c)}^{2}={a}^{2}+{b}^{2}+{c}^{2}+2bc+2ca+2ab$ | (2) |

Its contents may be expressed as the

Rule. The square of a sum is equal to the sum of the squares of all the summands plus the sum of all the double products of the summands in twos:

$$ |

This is true for any number of summands. The rule may be formulated also as

${(a+b+c+\mathrm{\dots})}^{2}=(a)a+(2a+b)b+(2a+2b+c)c+\mathrm{\dots}$ | (3) |

which in the case of four summands is

${(a+b+c+d)}^{2}=(a)a+(2a+b)b+(2a+2b+c)c+(2a+2b+2c+d)d.$ | (4) |

One can use the idea of (3) to find the , when one tries to arrange the polynomial into the form of the right hand side (http://planetmath.org/Equation) of (3).

Title | square of sum |

Canonical name | SquareOfSum |

Date of creation | 2013-03-22 15:32:03 |

Last modified on | 2013-03-22 15:32:03 |

Owner | pahio (2872) |

Last modified by | pahio (2872) |

Numerical id | 9 |

Author | pahio (2872) |

Entry type | Topic |

Classification | msc 30-00 |

Classification | msc 26-00 |

Classification | msc 11-00 |

Related topic | SquareRootOfPolynomial |

Related topic | DifferenceOfSquares |

Related topic | HeronianMeanIsBetweenGeometricAndArithmeticMean |

Related topic | ContraharmonicMeansAndPythagoreanHypotenuses |

Related topic | CompletingTheSquare |

Related topic | TriangleInequalityOfComplexNumbers |