=(a+b)(b+c)(c+a)

=(a+b+c)(ab+bc+ca)

(b-c)^2+b(a-c)^2+c(a-b)^2- a^3 -b^3 -c^3 +4abc 
=a[(b-c)^2-a^2)]+ b[(a-c)^2-b^2)]+c[(a-b)^2-c^2)]+4abc 
=a[(b-c)^2-a^2)]+ b[(a+c)^2-b^2)]+c[(a-b)^2-c^2)] 
=a(b-c-a)(b-c+a)+b(a+c-b)(a+b+c)+c(a+c... 
=[-a(b-c+a)+b(a+b+c)+c(a-b-c)](a+c-b) 
Bạn cứ tiếp tục phân tích cái vế trong ngoặc vuông đuọc (a+b-c)(b+c-a) là đc.

Đáp số : (a+c-b)(a+b-c)(b+c-a) 

:)) Thớt không search google nên bạn í search hộ thôi =.=

Đinh Tuấn Việt- sai dấu ở hàng thứ 3, còn 4abc nằm ở đâu?

\(a,=\left[\left(x+1\right)\left(x+5\right)\right]\left[\left(x+2\right)\left(x+4\right)\right]-40\\ =\left(x^2+6x+5\right)\left(x^2+6x+8\right)-40\\ =\left(x^2+6x\right)^2+13\left(x^2+6x\right)+40-40\\ =\left(x^2+6x\right)^2+13\left(x^2+6x\right)=\left(x^2+6x\right)\left(x^2+6x+13\right)\\ b,=a^2b^2\left(a-b\right)+b^2c^2\left(b-a+a-c\right)+c^2a^2\left(c-a\right)\\ =a^2b^2\left(a-b\right)-b^2c^2\left(a-b\right)-b^2c^2\left(c-a\right)+c^2a^2\left(c-a\right)\\ =\left(a-b\right)\left(a^2b^2-b^2c^2\right)-\left(c-a\right)\left(b^2c^2-c^2a^2\right)\\ =b^2\left(a-b\right)\left(a-c\right)\left(a+c\right)-c^2\left(c-a\right)\left(b-a\right)\left(b+a\right)\\ =\left(a-b\right)\left(a-c\right)\left[b^2\left(a+c\right)-c^2\left(b+a\right)\right]\\ =\left(a-b\right)\left(a-c\right)\left(a^2b+b^2c-b^2c+a^2c\right)\\ =a^2\left(a-b\right)\left(a-c\right)\left(b+c\right)\)

\(c,=\left(a+b\right)^3-3ab\left(a+b\right)+c^3-3abc\\ =\left(a+b+c\right)\left(a^2+2ab+b^2-ac-bc+c^2\right)-3ab\left(a+b+c\right)\\ =\left(a+b+c\right)\left(a^2+b^2+c^2-ab-bc-ac\right)\)

=a^2b-a^2c+b^2a-b^2c+c^2a-c^2b

=b(a^2-c^2)-a^2c+c^2a+b^2a-b^2c

=b(a-c)(a+c)-ac(a-c)+b^2(a-c)

=(a-c)(ba+bc-ac+b^2)

a) ta có: ab(a-b) + bc((b-a)+(a-c)) +ac(c-a) 

=ab(a-b) -bc(a-b) -bc(c-a) +ac(c-a) 
=(a-b)(ab-bc) +(c-a)(ac-bc) 
=(a-b) b (a-c) + (c-a) c (a-b) 
=(a-b)(a-c)(b-c) 

B),C),D) tương tự

ok mk nha!! 5645676577962353446456575675878768766734644565565464565575346456

(a+b)(b+c)(a-c)