a mũ 3 (b-c) + b mũ 3 (c-a) + c mũ 3 (a-b) giúp mình vs ạk PHân Tích Đa Thức Thành NHân TỬ

$a^3.(b-c)+b^3.(c-a)+c^3.(a-b)_{}$

$⇔a^3b-a^3c+b^3c-b^3a+c^3.(a-b)_{}$

$⇔(a^3b-b^3a)-(a^3c-b^3c)+c^3.(a-b)_{}$

$⇔ab.(a^2-b^2)-c.(a^3-b^3)+c^3.(a-b)_{}$

$⇔ab.(a-b)(a+b)-c.(a-b)(a^2+ab+b^2)+c^3.(a-b)_{}$

$⇔(a-b).[ ab.(a+b)-c.(a^2+ab+b^2)+c^3]_{}$

$⇔(a-b).(a^2b+ab^2-a^2c-abc-b^2c+c^3)_{}$

$⇔(a-b).[(a^2b-a^2c)+(ab^2-abc)-(b^2c-c^3) ]_{}$

$⇔(a-b).[a^2.(b-c)+ab.(b-c)-c.(b^2-c^2) ]_{}$

$⇔(a-b)(b-c).[a^2+ab-c.(b+c) ]_{}$

$⇔(a-b)(b-c).[(a-c)(a+c)+b.(a-c) ]_{}$

$⇔(a-b)(b-c)(a-c)(a+b+c)_{}$