Question

[Quang An Đinh]

Phân tích đa thức thành nhân tử:

a(b² + c²) - b(c² + a²) + c(a² + b²) -2abc

Answer 1

[Bùi Trang]

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

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