Leges binominales

Leges Binominales in Algebra elementaria dilatatae reri adiuvat

Leges

Leges Binominales solite hi tres sunt:

$(a+b)^{2}=a^{2}+2\cdot a\cdot b+b^{2}$	Primus Lex Binominale (Lex Additionis)
$(a-b)^{2}=a^{2}-2\cdot a\cdot b+b^{2}$	Secundus Lex Binominale  (Lex Subtractionis)
$(a+b)\cdot (a-b)=a^{2}-b^{2}$	Tertius Lex Binominale (Lex Additionis et Subtractionis)

Probatio Multiplicationis:

$(a+b)^{2}=(a+b)\cdot (a+b)=a\cdot a+a\cdot b+b\cdot a+b\cdot b=a^{2}+2\cdot a\cdot b+b^{2}$

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

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