É importante ressaltar que:
[tex](\text{a}+\text{b})^3=\text{a}^3+3\text{a}^2\text{b}+3\text{a}\text{b}^2+\text{b}^3[/tex]
[tex](\text{a}-\text{b})^3=\text{a}^3-3\text{a}^2\text{b}+3\text{a}\text{b}^2-\text{b}^3[/tex]
Façamos [tex]\text{A}=(\text{a}+1)^3-(\text{a}-2)^3[/tex]
Desta maneira, temos:
[tex]\text{A}=(\text{a}^3+3\text{a}^2+3\text{a}+1)-(\text{a}^3-6\text{a}^2+12\text{a}-8)[/tex]
Donde, obtemos:
[tex]\text{A}=\text{a}^3+3\text{a}^2+3\text{a}+1-\text{a}^3+6\text{a}^2-12\text{a}+8[/tex]
[tex]\text{A}=9\text{a}^2-9\text{a}+9=9\cdot(\text{a}^2-\text{a}+1)[/tex]
