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>