Question

Phân tích các đa thức sau thành nhân tử :

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

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

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

Answer 1

b)

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

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

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

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

Answer 2

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

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

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

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