Rule algebra.equations.quadratic.distr-square

Description
distribution for special products

Parameters
Buggy	no
Rewrite rule	yes
Siblings

Rewrite rule

(a+b)^2   ⇒   ((a^2)+((2·a)·b))+(b^2)
(a-b)^2   ⇒   ((a^2)-((2·a)·b))+(b^2)
(a+b)·(a-b)   ⇒   (a^2)-(b^2)
(a-b)·(a+b)   ⇒   (a^2)-(b^2)

Formal Mathematical Properties

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd"><OMBIND><OMS cd="quant1" name="forall"/><OMBVAR><OMV name="$0"/><OMV name="$1"/></OMBVAR><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="arith1" name="power"/><OMA><OMS cd="arith1" name="plus"/><OMV name="$0"/><OMV name="$1"/></OMA><OMI>2</OMI></OMA><OMA><OMS cd="arith1" name="plus"/><OMA><OMS cd="arith1" name="plus"/><OMA><OMS cd="arith1" name="power"/><OMV name="$0"/><OMI>2</OMI></OMA><OMA><OMS cd="arith1" name="times"/><OMA><OMS cd="arith1" name="times"/><OMI>2</OMI><OMV name="$0"/></OMA><OMV name="$1"/></OMA></OMA><OMA><OMS cd="arith1" name="power"/><OMV name="$1"/><OMI>2</OMI></OMA></OMA></OMA></OMBIND></OMOBJ></FMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd"><OMBIND><OMS cd="quant1" name="forall"/><OMBVAR><OMV name="$0"/><OMV name="$1"/></OMBVAR><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="arith1" name="power"/><OMA><OMS cd="arith1" name="minus"/><OMV name="$0"/><OMV name="$1"/></OMA><OMI>2</OMI></OMA><OMA><OMS cd="arith1" name="plus"/><OMA><OMS cd="arith1" name="minus"/><OMA><OMS cd="arith1" name="power"/><OMV name="$0"/><OMI>2</OMI></OMA><OMA><OMS cd="arith1" name="times"/><OMA><OMS cd="arith1" name="times"/><OMI>2</OMI><OMV name="$0"/></OMA><OMV name="$1"/></OMA></OMA><OMA><OMS cd="arith1" name="power"/><OMV name="$1"/><OMI>2</OMI></OMA></OMA></OMA></OMBIND></OMOBJ></FMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd"><OMBIND><OMS cd="quant1" name="forall"/><OMBVAR><OMV name="$0"/><OMV name="$1"/></OMBVAR><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="arith1" name="times"/><OMA><OMS cd="arith1" name="plus"/><OMV name="$0"/><OMV name="$1"/></OMA><OMA><OMS cd="arith1" name="minus"/><OMV name="$0"/><OMV name="$1"/></OMA></OMA><OMA><OMS cd="arith1" name="minus"/><OMA><OMS cd="arith1" name="power"/><OMV name="$0"/><OMI>2</OMI></OMA><OMA><OMS cd="arith1" name="power"/><OMV name="$1"/><OMI>2</OMI></OMA></OMA></OMA></OMBIND></OMOBJ></FMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd"><OMBIND><OMS cd="quant1" name="forall"/><OMBVAR><OMV name="$0"/><OMV name="$1"/></OMBVAR><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="arith1" name="times"/><OMA><OMS cd="arith1" name="minus"/><OMV name="$0"/><OMV name="$1"/></OMA><OMA><OMS cd="arith1" name="plus"/><OMV name="$0"/><OMV name="$1"/></OMA></OMA><OMA><OMS cd="arith1" name="minus"/><OMA><OMS cd="arith1" name="power"/><OMV name="$0"/><OMI>2</OMI></OMA><OMA><OMS cd="arith1" name="power"/><OMV name="$1"/><OMI>2</OMI></OMA></OMA></OMA></OMBIND></OMOBJ></FMP>