Làm tính nhân:

$a) \left(\frac{1}{2}x+y\right)\left(\frac{1}{2}x+y\right)$

$b) \left(x-\frac{1}{2}y\right)\left(x-\frac{1}{2}y\right)$

Giải:

$$\begin{gathered} a) \left(\frac{1}{2}x+y\right)\left(\frac{1}{2}x+y\right) \\ =\frac{1}{2}x.\frac{1}{2}x+\frac{1}{2}x.y+y.\frac{1}{2}x+y.y \\ =\frac{1}{4}{x}^2+\frac{1}{2}xy+\frac{1}{2}xy+y^2 \\ =\frac{1}{4}{x}^2+xy+y^2 \end{gathered}$$

$$\begin{gathered} b) \left(x-\frac{1}{2}y\right)\left(x-\frac{1}{2}y\right) \\ =x.x+x\left(-\frac{1}{2}y\right)+\left(-\frac{1}{2}y.x\right)+\left(-\frac{1}{2}y\right)\left(-\frac{1}{2}y\right) \\ =x^2-\frac{1}{2}xy-\frac{1}{2}xy+\frac{1}{4}{y}^2 \\ =x^2-xy+\frac{1}{4}{y}^2 \end{gathered}$$