Áp dụng hằng đẳng thức đáng nhớ để thực hiện phép chia:

$$\begin{gathered} a) (x^2 + 2xy + y^2) : (x + y); \\ b) (125x^3 + 1) : (5x + 1); \\ c) (x^2 – 2xy + y^2) : (y – x); \end{gathered}$$

Giải:

$a) (x^2 + 2xy + y^2) : (x + y)={(x + y)}^2 : (x + y) = x + y.$

$$\begin{gathered} b) (125x^3 + 1) : (5x + 1) \\ =[{\left(5x\right)}^3 + 1] : (5x + 1) \\ = {\left(5x\right)}^2 – 5x + 1 \\ = 25x^2 – 5x + 1. \end{gathered}$$

$$\begin{gathered} c) (x^2 – 2xy + y^2) : (y – x) \\ = {(x – y)}^2 : [-(x – y)] \\ = - (x – y) = y – x \\ Hoặc (x^2 – 2xy + y^2) : (y – x) \\ = (y^2 – 2xy + x^2) : (y – x) \\ = {(y – x)}^2 : (y – x) \\ = y - x. \end{gathered}$$