Question

Phân tích đa thức sau thành nhân tử:

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

Answer 1

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

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

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

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

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

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

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