Question

Rút gọn

\(\left(x+y+1\right)^3-\left(x+y-1\right)^3-6\left(x+y\right)^2\)

Answer 1

`(x+y+1)^3 - (x+y-1)^3 - 6(x+y)^2`

`=(x+y+1-x-y+1)[(x+y+1)^2 + (x+y+1)(x+y-1) + (x+y-1)^2] - 6(x+y)^2`

`=2(x^2+y^2 + 2xy+2x+2y + 1 + x^2 + 2xy +y^2 - 1 + x^2 + y^2 + 1 +2xy - 2x - 2y) - 6(x^2 + 2xy + y^2)`

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

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

`=2`

Answer 2

\(=x^3+y^3+1-x^3-y^3+1-6\left(x^2+2xy+y^2\right)\\ =-6x^2-12xy+-6y^2+2\)