1. Rút gọn biểu thức sau a) (x+y+z).(x-y+z).(x+y-z).(x-y-z)

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1. Giải thích các bước giải:

   `(x+y+z).(x-y+z).(x+y-z).(x-y-z)`

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

   `=(x+z)^2.(x-z)^2-y^2.(x+z)^2-y^2.(x-z)^2+y^4`

   `=[(x+z)(x-z)]^2-y^2[(x+z)^2+(x-z)^2]+y^4`

   `=(x^2-z^2)^2-y^2(x^2+2xz+z^2+x^2-2xz+z^2)+y^4`

   `=x^4+z^4+2x^2z^2-(2x^2+2z^2)y^2+y^4`

   `=x^4+y^4+z^4-2x^2y^2-4y^2z^2`

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2. `a) (x+y+z).(x-y+z).(x+y-z).(x-y-z)`

   `=[(x+y+z).(x-y-z)].[(x-y+z).(x+y-z)]`

   `={[x+(y+z)].[x-(y+z)]}.{[x-(y-z)].[x+(y-z)]}`

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

   `=x^4 -[x(y+z)]^2 -[x(y-z)]^2 +[(y+z)^2 .(y-z)^2 ]`

   `=x^4 -(xy++zy)^2 -(xy-yz)^2 +[(y+z).(y-z)]^2`

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

   `=x^4 -2x^2 y^2 -2z^2 y^2  +y^4 -2y^2 z^2 +z^4`

   `=x^4 +y^4 + z^4 -2x^2 y^2 -4y^2 z^2`

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