Rút gọn biểu thức chứa đơn thức nhân đa thức

a) \(4x^2(5x^2 + 3) - 6x(3x^3 - 2x + 1) - 5x^3(2x - 1)\) \(= 4x^2 \cdot 5x^2 + 4x^2 \cdot 3 - (6x \cdot 3x^3 + 6x \cdot (-2x) + 6x \cdot 1) - (5x^3 \cdot 2x + 5x^3 \cdot (-1))\) \(= 20x^4 + 12x^2 - (18x^4 - 12x^2 + 6x) - (10x^4 - 5x^3)\) \(= 20x^4 + 12x^2 - 18x^4 + 12x^2 - 6x - 10x^4 + 5x^3\) \(= (20x^4 - 18x^4 - 10x^4) + 5x^3 + (12x^2 + 12x^2) - 6x\) \(= -8x^4 + 5x^3 + 24x^2 - 6x\) b) \(\dfrac{3}{2}x\left(x^2 - \dfrac{2}{3}x + 2\right) - \dfrac{5}{3}x^2\left(x + \dfrac{6}{5}\right)\) \(= \dfrac{3}{2}x \cdot x^2 + \dfrac{3}{2}x \cdot \left(-\dfrac{2}{3}x\right) + \dfrac{3}{2}x \cdot 2 - \left(\dfrac{5}{3}x^2 \cdot x + \dfrac{5}{3}x^2 \cdot \dfrac{6}{5}\right)\) \(= \dfrac{3}{2}x^3 - x^2 + 3x - \left(\dfrac{5}{3}x^3 + 2x^2\right)\) \(= \dfrac{3}{2}x^3 - x^2 + 3x - \dfrac{5}{3}x^3 - 2x^2\) \(= \left(\dfrac{3}{2}x^3 - \dfrac{5}{3}x^3\right) + (-x^2 - 2x^2) + 3x\) \(= \left(\dfrac{9}{6}x^3 - \dfrac{10}{6}x^3\right) - 3x^2 + 3x\) \(= -\dfrac{1}{6}x^3 - 3x^2 + 3x\)