Phân tích thành nhân tử ab (a+b) -bc (b+c) +ac (a-c)

* Hướng dẫn giải

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

$$\begin{gathered} =ab\left(a+b\right)-b^{2}c-b{c}^2+a^{2}c-a{c}^2 \\ =ab\left(a+b\right)+\left(a^{2}c-b^{2}c\right)-\left(a{c}^2+b{c}^2\right) \\ =ab\left(a+b\right)+c\left(a^2-b^2\right)-c^2\left(a+b\right) \\ =ab\left(a+b\right)+c\left(a-b\right)\left(a+b\right)-c^2\left(a+b\right) \\ =\left(a+b\right)\left(ab+ac-bc-c^2\right) \\ =\left(a+b\right)\left[\left(ab-bc\right)+\left(ac-c^2\right)\right] \\ =\left(a+b\right)\left[b\left(a-c\right)+c\left(a-c\right)\right] \\ =\left(a+b\right)\left(b+c\right)\left(a-c\right) \end{gathered}$$