Tính nhanh:

$$\begin{gathered} a) (4x^2 – 9y^2) : (2x – 3y); \\ b) (27x^3 – 1) : (3x – 1); \\ c) (8x^3 + 1) : (4x^2 – 2x + 1); \\ d) (x^2 – 3x + xy -3y) : (x + y); \end{gathered}$$

Giải:

$$\begin{gathered} a) (4x^2 – 9y^2) : (2x – 3y) \\ =[{\left(2x\right)}^2 – {\left(3y\right)}^2] : (2x – 3y) \\ = 2x + 3y \end{gathered}$$

$$\begin{gathered} b) (27x^3 – 1) : (3x – 1) \\ = [{\left(3x\right)}^3 – 1] : (3x – 1) \\ = {\left(3x\right)}^2 + 3x + 1 \\ = 9x^2 + 3x + 1 \end{gathered}$$

$$\begin{gathered} c) (8x^3 + 1) : (4x^2 – 2x + 1) \\ = [{\left(2x\right)}^3 + 1] : (4x^2 – 2x + 1) \\ = (2x + 1\left)\right[{\left(2x\right)}^2 – 2x + 1] : (4x^2 – 2x + 1) \\ = (2x + 1\left)\right(4x^2 – 2x + 1) : (4x^2 – 2x + 1) \\ = 2x + 1 \end{gathered}$$

$$\begin{gathered} d) (x^2 – 3x + xy -3y) : (x + y) \\ = [(x^2 + xy) – (3x + 3y)] : (x + y) \\ = [x(x + y) – 3(x + y)] : (x + y) \\ = (x + y\left)\right(x – 3) : (x + y) \\ = x – 3 \end{gathered}$$