Làm tính chia: [5(a – b)^3 + 2(a – b)^2] : (b – a)^2

* Hướng dẫn giải

Ta có: b – a= - (a- b) nên

${\left(b-a\right)}^2=\left[-{\left(a-b\right)}^2\right]={\left(-1\right)}^2.{\left(a-b\right)}^2={\left(a-b\right)}^2$

$$\begin{gathered} \left[5{\left(a-b\right)}^3+2{\left(a-b\right)}^2\right]:{\left(b-a\right)}^2 \\ =\left[5{\left(a-b\right)}^3+2{\left(a-b\right)}^2\right]:{\left(a-b\right)}^2 \\ =5{\left(a-b\right)}^3:{\left(a-b\right)}^2+2{\left(a-b\right)}^2:{\left(a-b\right)}^2 \\ =5\left(a-b\right)+2 \end{gathered}$$