Đáp án:

Giải thích các bước giải:

`a.`

`A=(x-1)^3-(x+1)^3`

`=[(x-1)-(x+1)][(x-1)^2+(x-1)(x+1)+(x+1)^2]`

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

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

`b.`

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

`=[(x+1)+(x-1)]^3`

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

`=(2x)^3=8x^3.`

`c.`

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

`=[(x-y)-x]^3`

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

`=(-y)^3=-y^3`

`***` Áp dụng các HĐT:

`(A+B)^2=A^2+2AB+B^2`

`A^2-B^2=(A-B)(A+B)`

`A^3-B^3=(A-B)(A^2+AB+B^2)`

`(A+B)^3=A^3+3A^2B+3AB^2+B^3`

`(A-B)^3=A^3-3A^2B+3AB^2-B^3`