Respostas

  • Usuário do Brainly
2013-01-08T20:48:41-02:00

É importante ressaltar que:

 

(\text{a}+\text{b})^3=\text{a}^3+3\text{a}^2\text{b}+3\text{a}\text{b}^2+\text{b}^3

 

(\text{a}-\text{b})^3=\text{a}^3-3\text{a}^2\text{b}+3\text{a}\text{b}^2-\text{b}^3

 

Façamos \text{A}=(\text{a}+1)^3-(\text{a}-2)^3

 

Desta maneira, temos:

 

\text{A}=(\text{a}^3+3\text{a}^2+3\text{a}+1)-(\text{a}^3-6\text{a}^2+12\text{a}-8)

 

Donde, obtemos:

 

\text{A}=\text{a}^3+3\text{a}^2+3\text{a}+1-\text{a}^3+6\text{a}^2-12\text{a}+8

 

\text{A}=9\text{a}^2-9\text{a}+9=9\cdot(\text{a}^2-\text{a}+1)