Phân tích đa thức thành nhân tử (x^2+y^2+xy)^2-x^2y^2-y^2z^2-x^2z^2

`(x^2+y^2+xy)^2-x^2y^2-y^2z^2-x^2z^2`

` = x^4 + 2x^3y + 3x^2y^2 + 2xy^3 + y^4 – x^2y^2 – y^2z^2 – x^2z^2`

` = x^4 + y^4 + 2x^3y + 2x^2y^2 + 2xy^3 – y^2z^2 – x^2z^2`

` = (x^4 + 2x^3y + x^2y^2 – x^2z^2) + (x^2y^2 + 2xy^3 + y^4 – y^2z^2)`

` = x^2 . (x^2 + 2xy + y^2 – z^2) + y^2 . (x^2 + 2xy + y^2 – z^2)`

` = x^2 . [(x+y)^2 – z^2] + y^2 . [(x+y)^2 – z^2]`

` = (x^2 + y^2) . [(x+y)^2 – z^2]`

` = (x^2 + y^2)(x + y -z )(x + y+z)`