Đáp án+Giải thích các bước giải:

5,

`(y-x)^3-(2x-y)^3`

`=(y^3-3y^2x+3yx^2-x^3)-(8x^3-12x^2+6xy^2-y^3)`

`=y^3-3y^2x+3yx^2-x^3-8x^3+12x^2y-6xy^2+y^3`

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

`=2y^3-9xy^2+15x^2y-9x^3`

6,

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

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

`=8x^3+12x^2y+6xy^2+y^3-2y^3+6xy^2-6x^2y+2x^3`

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

`=10x^3+6x^2y+12xy^2-y^3`

7,

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

`=(8x^3-36x^2+54x-27)-2x(4x^2+4x+1)`

`=8x^3-36x^2+54x-27-8x^3-8x^2-2x`

`=(8x^3-8x^3)-(36x^2+8x^2)+(54x-2x)-27`

`=-44x^2+52x-27`

8,

`(3x-1)^3-27x^2(x+1)`

`=(27x^3-27x^2+9x-1)-(27x^3+27x^2)`

`=27x^3-27x^2+9x-1-27x^3-27x^2`

`=(27x^3-27x^3)-(27x^2+27x^2)+9x-1`

`=-54x^2+9x-1`

9,

`(2x+1)^3-8x(x-1)^2`

`=(8x^3+12x^2+6x+1)-8x(x^2-2x+1)`

`=8x^3+12x^2+6x+1-8x^3+16x^2-8x`

`=(8x^3-8x^3)+(12x^2+16x^2)+(6x-8x)+1`

`=28x^2-2x+1`