Phân tích các đa thức sau thành nhân tử:

$$\begin{gathered} a) 3x-6y; \\ b) \frac{2}{5}{x}^2+5x^3+x^{2}y; \\ c) 14x^{2}y-21x{y}^2+28x^2{y}^2; \\ d) \frac{2}{5}x\left(y-1\right)-\frac{2}{5}y\left(y-1\right); \\ e) 10x(x-y)-8y(y-x); \end{gathered}$$

Giải:

$a) 3x-6y = 3.x-3.2y=3(x-2y)$

$b) \frac{2}{5}{x}^2+5x^3+x^{2}y=x^2\left(\frac{2}{5}+5x+y\right)$

$$\begin{gathered} c) 14x^{2}y-21x{y}^2+28x^2{y}^2 \\ =7xy.2x-7xy.3y+7xy.4xy \\ =7xy(2x-3y+4xy) \end{gathered}$$

$d) \frac{2}{5}x\left(y-1\right)-\frac{2}{5}y\left(y-1\right)=\frac{2}{5}\left(y-1\right)\left(x-y\right)$

$$\begin{gathered} e) 10x(x-y)-8y(y-x) \\ =10x(x-y)-8y[-(x-y)] \\ =10x(x-y)+8y(x-y) \\ =2(x-y\left)\right(5x+4y) \end{gathered}$$