Podemos expandir (a-1)³ utilizando a propriedade distributiva da multiplicação:
[tex]\sf (a-1)^3~=~(a-1)\cdot (a-1)\cdot (a-1)\\\\\\Aplicando~a~propriedade~distributiva~nos~dois~primeiros~termos\\\\\\(a-1)^3~=~\Big(~a\cdot a~+~a\cdot (-1)~+~(-1)\cdot a~+~(-1)\cdot (-1)~\Big)\cdot (a-1)\\\\\\(a-1)^3~=~\Big(~a^2~-~a~-~a~+~1~\Big)\cdot (a-1)\\\\\\(a-1)^3~=~(a^2~-~2a~+~1)\cdot (a-1)\\\\\\Aplicando~novamente~a~propriedade~nos~dois~termos~restantes:\\\\\\(a-1)^3\,=\,a^2\cdot a~+~a^2\cdot (-1)~+~(-2a)\cdot a~+~(-2a)\cdot (-1)~+~1\cdot a~+~1\cdot (-1)[/tex]
[tex]\sf (a-1)^2~=~a^3~-~a^2~-~2a^2~+~2a~+~a~-~1\\\\\\\boxed{\sf (a-1)^2~=~a^3~-~3a^2 ~+~3a~-~1}[/tex]
[tex]\Huge{\begin{array}{c}\Delta \tt{\!\!\!\!\!\!\,\,o}\!\!\!\!\!\!\!\!\:\,\perp\end{array}}Qualquer~d\acute{u}vida,~deixe~ um~coment\acute{a}rio[/tex]
