Question

resolva (a + 1) ao cubo - (a - 2) ao cubo???

Answer 1

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:

 

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

 

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