Rút gọn các biểu thức sau:
a) 4x2(5x2 + 3) – 6x(3x3 – 2x + 1) – 5x3 (2x – 1)
b) \(\dfrac{3}{2}x\left( {{x^2} – \dfrac{2}{3}x + 2} \right) – \dfrac{5}{3}{x^2}(x + \dfrac{6}{5})\)
a) 4x2(5x2 + 3) – 6x(3x3 – 2x + 1) – 5x3 (2x – 1)
= 4x2 . 5x2 + 4x2 . 3 – [6x . 3x3 + 6x . (-2x) + 6x . 1] – [5x3 . 2x + 5x3 . (-1)]
= 20x4 + 12x2 – (18x4 – 12x2 + 6x) – (10x4 – 5x3)
= 20x4 + 12x2 – 18x4 + 12x2 – 6x – 10x4 + 5x3
= (20x4 – 18x4 – 10x4 ) + 5x3 + (12x2 + 12x2 ) – 6x
= -8x4 + 5x3 + 24x2 – 6x
\(\begin{array}{l}b)\dfrac{3}{2}x\left( {{x^2} – \dfrac{2}{3}x + 2} \right) – \dfrac{5}{3}{x^2}(x + \dfrac{6}{5})\\ = \dfrac{3}{2}x.{x^2} + \dfrac{3}{2}x.( – \dfrac{2}{3}x) + \dfrac{3}{2}x.2 – (\dfrac{5}{3}{x^2}.x + \dfrac{5}{3}{x^2}.\dfrac{6}{5})\\ = \dfrac{3}{2}{x^3} – {x^2} + 3x – (\dfrac{5}{3}{x^3} + 2{x^2})\\ = \dfrac{3}{2}{x^3} – {x^2} + 3x – \dfrac{5}{3}{x^3} – 2{x^2}\\ = (\dfrac{3}{2}{x^3} – \dfrac{5}{3}{x^3}) + ( – {x^2} – 2{x^2}) + 3x\\ = \dfrac{{ – 1}}{6}{x^3} – 3{x^2} + 3x\end{array}\)