\(A=a\left[\left(b-c\right)^2-a^2\right]+b\left[\left(c-a\right)^2-b^2\right]+c\left[\left(a-b\right)^2-c^2\right]+4abc\)

\(=a\left(b-c+a\right)\left(b-c-a\right)+b\left(c-a+b\right)\left(c-a-b\right)+c\left(a-b+c\right)\left(a-b-c\right)+4abc\)

\(=\left(a+b-c\right)\left(ab-ac-a^2-bc+ab-b^2\right)+c\left(a^2-2ab+b^2-c^2+4ab\right)\)

\(=\left(a+b-c\right)\left[-c\left(a+b\right)-\left(a-b\right)^2\right]+c\left[\left(a+b\right)^2-c^2\right]\)

\(=\left(a+b-c\right)\left(-ca-cb-a^2+2ab-b^2+ac+cb+c^2\right)\)

\(=\left(a+b-c\right)\left(c^2-\left(a-b\right)^2\right)\)

\(=\left(a+b-c\right)\left(c+a-b\right)\left(a+b-c\right)\)

a(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) 
em cu tiếp tục phân tích cái vế trong ngoặc vuông đuọc (a+b-c)(b+c-a) la d'c em nha 
dap so la :(a+c-b)(a+b-c)(b+c-a) 

           tick nha !!!

pá đạo quá lớp 7 làm bài lớp 8 ak

CHTT nha bạn ! 

\(=\left(a+b\right)\left(b+c\right)\left(c+a\right)\)

nhân ngược lại ra hay đặt ản thì tùy nhé =))

\(a,c\left(a+b\right)^2+b\left(c+a\right)^2+a\left(b+c\right)^2-4abc\)

\(=c\left(a+b\right)^2+bc^2+2abc+a^2b+ab^2+2abc+ac^2-4abc\)

\(=c\left(a+b\right)^2+\left(bc^2+ac^2\right)+\left(a^2b+ab^2\right)\)

\(=c\left(a+b\right)^2+c^2\left(a+b\right)+ab\left(a+b\right)\)

\(=\left(a+b\right)\left(ac+cb+c^2+ab\right)\)

\(=\left(a+b\right)\left[c\left(a+c\right)+b\left(a+c\right)\right]\)

\(=\left(a+b\right)\left(a+c\right)\left(b+c\right)\)

(a(b-c)^2 + b(c-a)^2 + c(a-b)^2) - (a^3 + b^3 + c^3) + 4abc

= a(b^2 - 2bc + c^2) + b(c^2 - 2ac + a^2) + c(a^2 - 2ab + b^2) - (a^3 + b^3 + c^3) + 4abc

= ab^2 - 2abc + ac^2 + bc^2 - 2abc + ba^2 + ca^2 - 2abc + cb^2 - a^3 - b^3 - c^3 + 4abc

= ab^2 + ac^2 + bc^2 + ba^2 + ca^2 + cb^2 - a^3 - b^3 - c^3 + 4abc - 6abc

= a(b^2 + c^2 + a^2) + b(a^2 + c^2 + b^2) + c(a^2 + b^2 + c^2) - (a^3 + b^3 + c^3) - 2abc

= a^3 + b^3 + c^3 + a^2b + ab^2 + a^2c + ac^2 + b^2c + bc^2 - a^3 - b^3 - c^3 - 2abc

= a^2b + ab^2 + a^2c + ac^2 + b^2c + bc^2 - 2abc

= ab(a + b) + ac(a + c) + bc(b + c) - 2abc

= (a + b)(ab - ac + bc) - 2abc

Vậy, ta có thể viết bài toán dưới dạng nhân tử là: (a + b)(ab - ac + bc) - 2abc.

\(a\left(b-c\right)^2+b\left(c-a\right)^2+c\left(a-b\right)^2-a^3-b^3-c^3+4abc\)

\(=a\left(b-c\right)^2-a^3+4abc+b\left(c-a\right)^2-b^3+c\left(a-b\right)^2-c^3\)

\(=a\left[\left(b-c\right)^2+4bc-a^2\right]+b\left[\left(c-a\right)^2-b^2\right]+c\left[\left(a-b\right)^2-c^2\right]\)

\(=a\left[\left(b+c\right)^2-a^2\right]+b\left[\left(c-a\right)^2-b^2\right]+c\left[\left(a-b\right)^2-c^2\right]\)

\(=a\left(b+c+a\right)\left(b+c-a\right)+b\left(c-a+b\right)\left(c-a-b\right)+c\left(a-b+c\right)\left(a-b-c\right)\)

\(=\left(b+c-a\right)\left[a\left(b+c+a\right)+b\left(c-a-b\right)\right]+c\left(a-b+c\right)\left(a-b-c\right)\)

\(=\left(b+c-a\right)\left[ab+ac+a^2+bc-ab-b^2\right]+c\left(a-b+c\right)\left(a-b-c\right)\)

\(=\left(b+c-a\right)\left[c\left(a+b\right)+\left(a-b\right)\left(a+b\right)\right]+c\left(a-b+c\right)\left(a-b-c\right)\)

\(=\left(b+c-a\right)\left(a+b\right)\left(a-b+c\right)+c\left(a-b+c\right)\left(a-b-c\right)\)

\(=\left(a-b+c\right)\left[b^2-\left(a-c\right)^2\right]\)

\(=\left(a-b+c\right)\left(b+a-c\right)\left(b-a+c\right)\)