Làm tính nhân:

a) $x^2\left(5x^3-x-\frac{1}{2}\right)$

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

c) $\left(4x^3-5xy+2x\right)\left(-\frac{1}{2}xy\right)$

Giải:

$$\begin{gathered} a) x^2\left(5x^3-x-\frac{1}{2}\right) \\ =x^{2}5x^3+x^2\left(-x\right)-\frac{1}{2}{x}^2 \\ =5x^5-x^3-\frac{1}{2}{x}^2 \end{gathered}$$

$$\begin{gathered} b) \left(3xy-x^2+y\right)\frac{2}{3}{x}^{2}y \\ =\frac{2}{3}{x}^{2}y.3xy+\frac{2}{3}{x}^{2}y\left(-x^2\right)+\frac{2}{3}{x}^{2}y.y \\ =\frac{2}{3}{x}^2{y}^2-\frac{2}{3}{x}^{4}y+\frac{2}{3}{x}^2{y}^2 \end{gathered}$$

$$\begin{gathered} c) \left(4x^3-5xy+2x\right)\left(-\frac{1}{2}xy\right) \\ =4x^3\left(-\frac{1}{2}xy\right)-5xy\left(-\frac{1}{2}xy\right)+2x\left(-\frac{1}{2}xy\right) \\ =-2x^4+\frac{5}{2}{x}^2{y}^2-x^{2}y \end{gathered}$$