Hướng dẫn trả lời:
$\text{$a^{2}.(b - c) + b^{2}.(c - a) + c^{2}.(a - b).$}$
$\text{= $a^{2}b - a^2c + b^2c - ab^2 + c^{2}.(a - b).$}$
$\text{= $a^{2}b - ab^2 + a^2c - b^2c + c^{2}.(a - b).$}$
$\text{= $ab.(a - b) - c.(a^2 - b^2) + c^{2}.(a - b).$}$
$\text{= (a - b).(ab + $c^{2}$) - c.($a^2 - b^2$).}$
$\text{= (a - b).(ab + $c^{2}$) - c.(a - b).(a + b).}$
$\text{= (a - b).[ab + $c^{2}$ - c.(a + b)].}$
$\text{= (a - b).(ab + $c^{2}$ - ac - bc).}$
$\text{= (a - b).[(ab - bc) + ($c^{2}$ - ac)].}$
$\text{= (a - b).[(b.(a - c) + c.(c - a)].}$
$\text{= (a - b).[(b.(a - c) - c.(a - c)].}$
$\text{= (a - b).(a - c).(b - c).}$
$\text{Vậy $a^{2}.(b - c) + b^{2}.(c - a) + c^{2}.(a - b)$ = (a - b).(a - c).(b - c).}$
