Làm tính nhân:

$$\begin{gathered} a. 5x^2.(3x^2 – 7x + 2) \\ b. \frac{2}{3}xy.\left(2x^{2}y-3xy+y^2\right) \end{gathered}$$

Giải:

$$\begin{gathered} a. 5x^2.(3x^2 – 7x + 2) \\ = 5x^2.3x^2 + 5x^2.(-7x) + 5x^2.2 \\ = (5.3).(x^2.x^2) + [5.(-7\left)\right].(x^2.x) + (5.2).x^2 \\ = 15x^{2+2}+ (-35).x^{2+1} + 10.x^2 \\ = 15x^4 – 35x^3 + 10x^2 \end{gathered}$$

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