Question

Phân tích đa thức sau thành nhân tử

\(k,ab\left(a+b\right)-bc\left(b+c\right)-ca\left(c-a\right)\)

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

Answer 1

k: \(=a^2b+ab^2-b^2c-bc^2-c^2a+ca^2\)

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

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

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

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

l: \(=a^2b-a^2c+b^2c-b^2a+c^2a-c^2b\)

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

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

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

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