Question

Rút gọn các biểu thứ sau

1) (x + 1)'3 - (x - 4)(x + 4) - x'3

2) (x + 2)'3 - x(x + 3)(x - 3) - 12x'2 -8

3) (x - 2)'3 - x(x - 2)(x + 2) + 6x(x - 3)

4) x(x - 5)(x + 5) - (x - 5)'3 + 100x

Answer 1

`1)(x+1)^3-(x-4)(x+4)-x^3`

`=(x^3+3x^2+3x+1)-(x^2-16)-x^3`

`=x^3+3x^2+3x+1-x^2+16-x^3`

`=2x^2+3x+17`

`2)(x+2)^3-x(x+3)(x-3)-12x^2-8`

`=(x^3+6x^2+12x+8)-x(x^2-9)-12x^2-8`

`=x^3+6x^2+12x+8-x^3+9x-12x^2-8`

`=-6x^2+21x` 

`3)(x-2)^3-x(x-2)(x+2)+6x(x-3)`

`=(x^3-6x^2+12x-8)-x(x^2-4)+6x^2-18x`

`=x^3-6x^2+12x-8-x^3+4x+6x^2-18x`

`=-2x-8`

`4)x(x-5)(x+5)-(x-5)^3+100x`

`=x(x^2-25)-(x^3-15x^2+75x-125)+100x`

`=x^3-25x-x^3+15x^2-75x+125+100x`

`=15x^2+125`

Answer 2

`(x+1)^3 - (x-4)(x+4) - x^3`

`= x^3 + 3x^2 + 3x + 1 - (x^2 - 16) - x^3`

`=x^3 + 3x^2 + 3x + 1 - x^2 + 16 - x^3`

`= 2x^2 + 3x +17`

`(x+2)^3 - x(x + 3)(x-3) - 12x^3 - 8`

`= x^3 + 6x^2 + 12x + 8 - x(x^2 - 9) - 12x^2 - 8`

`= x^3 + 6x^2 + 12x + 8 - x^3 + 9x - 12x^2 - 8`

`= (x^3 - x^3 ) + (6x^2-12x^2) + (12x + 9x) + (8 - 8)`

`=  -6x^2 + 21x `

`(x-2)^3 - x(x-2)(x+2) +6x(x-3)`

`= x^3 -6x^2 + 12x -8 -x(x^2 - 4) + 6x^2 - 18x`

`= x^3 - 6x^2 + 12x - 8 -x^3 + 4x + 6x^2 - 18x`

`=(x^3 - x^3) - (6x^2 - 6x^2) + (12x + 4x - 18x) - 8`

`= -2x - 8`

`x(x-5)(x+5) - (x-5)^3 + 100x`

`= x(x^2 - 25) - (x^3 - 15x^2 + 75x - 25 ) + 100x`

`= x^3 - 25x - x^3 + 15x^2 - 75x + 25 + 100x`

`= (x^3 - x^3) + 15x^2 - (25x + 75x - 100x) + 25`

`= 15x^2 +25`