Rút gọn các biểu thức sau: a) 4x2(5x2 + 3) - 6x (3x2 - 2x + 1) - 5x3(2x - 1);

* Hướng dẫn giải

Lời giải:

a) 4x²(5x² + 3) - 6x (3x² - 2x + 1) - 5x³(2x - 1)

= 4x².5x² + 4x².3 + (-6x).3x² + (-6x).(-2x) + (-6x).1 + (-5x³).2x + (-5x³).(-1)

= 20x⁴ + 12x² + (-18x³) + 12x² + (-6x) + (-10x⁴) + 5x³

= 20x⁴ + 12x² - 18x³ + 12x² - 6x - 10x⁴ + 5x³

= (20x⁴ - 10x⁴) + (-18x³ + 5x³) + (12x² + 12x²) - 6x

= 10x⁴ + (-13x³) + 24x² - 6x

= 10x⁴ -13x³ + 24x² - 6x

b) $\frac{3}{2}x(x^2-\frac{2}{3}x+2)-\frac{5}{3}{x}^2(x+\frac{6}{5})$

= $\frac{3}{2}$x.x² + $[\frac{3}{2}.\left(\frac{-2}{3}\right)]$x.x +$\frac{3}{2}$x.2 + $\left(\frac{-5}{3}{x}^2\right)$.x +$\left(\frac{-5}{3}{x}^2\right)$.$\frac{6}{5}$

= $\frac{3}{2}$x³ - x² + 3x $-\frac{5}{3}$x³ - 2x²

= $(\frac{3}{2}{x}^3-\frac{5}{3}{x}^3)$ + (-x² - 2x²) + 3x

= $(\frac{9}{6}{x}^3-\frac{10}{6}{x}^3)$ + (-3x²) + 3x

= -1/6x³ - 3x² + 3x