Question

1) Rút gọn biểu thức sau :

a) (x + 1)³ - (x + 3)² . (x + 1) + 4x² + 8

b) (x - 2).(x² + 2x + 4) - (x + 1)³ + 3.(x - 1).(x + 1)

c) ( x⁴ - 5² + 25).(x² + 5) - (2 + x²)³ + 3.(1 + x²)²Mọi người giúp giùm em !!! Cảm ơn mng !

 

 

Answer 1

(x + 1)³ - (x + 3)².(x + 1) + 4x² + 8 = x³ + 3x² + 3x + 1 - (x² + 6x + 9)(x + 1) + 4x² + 8

= x³ + 7x² + 3x + 9 - (x³ + 6x² + 9x + x² + 6x + 9) = -12x

(x - 2)(x² + 2x + 4) - (x + 1)³ + 3(x - 1)(x + 1) = x³ + 2x² + 4x - 2x² - 4x - 8 - x³ - 3x² - 3x - 1 + 3(x² - 1) 

= -9 - 3x² - 3x + 3x² - 3 = -12 - 3x

(x⁴ - 5² + 25)(x² + 5) - (2 + x²)³ + 3(1 + x²)² = x⁶ + 5x⁴ - 8 - 12x² - 6x⁴ - x⁶ + 3(1 + 2x² + x⁴) = -x⁴ - 12x² - 8 + 3 + 6x² + 3x⁴

= 2x⁴ - 6x² - 5