例2 计算：
图16.2-1
(1) $(-4x^2)(3x+1)$；
(2) $(\dfrac{2}{3}ab^2 - 2ab) · \dfrac{1}{2}ab$；
(3) $(x - 3y)(xy^2)^2$；
(4) $x(y - z) - y(z - x) + z(x - y)$．
解：(1) $\quad (-4x^2)(3x + 1)$
$\quad = (-4x^2)(3x) + (-4x^2) · 1$
$\quad = (-4 × 3)(x^2 · x) + (-4x^2)$
$\quad = -12x^3 - 4x^2$；

(2) $\quad (\dfrac{2}{3}ab^2 - 2ab) · \dfrac{1}{2}ab$
$\quad = \dfrac{2}{3}ab^2 · \dfrac{1}{2}ab + (-2ab) · \dfrac{1}{2}ab$
$\quad = \dfrac{1}{3}a^2b^3 - a^2b^2$；

(3) $\quad (x - 3y)(xy^2)^2$
$\quad = (x - 3y) · x^2y^4$
$\quad = x · x^2y^4 + (-3y) · x^2y^4$
$\quad = x^3y^4 - 3x^2y^5$；
(4) $\quad x(y - z) - y(z - x) + z(x - y)$
$\quad = xy + x(-z) + (-y)z + (-y)(-x) + zx + z(-y)$
$\quad = xy - xz - yz + yx + zx - zy$
$\quad = 2xy - 2yz$．