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Đáp án:
`xy(x + y) + yz(y + z) + zx(z + x) + 2xyz` `=` `(x + y)(y + z)(x + z).`
Giải thích các bước giải:
`xy(x + y) + yz(y + z) + zx(z + x) + 2xyz`
`= xy(x + y) + y^2z + yz^2 + z^2x + zx^2 + 2xyz`
`= xy(x + y) + (y^2z + x^2z + 2xyz) + yz^2 + z^2x`
`= xy(x + y) + z(y^2 + x^2 + 2xy) + z^2(x + y)`
`= xy(x + y) + z(x + y)^2 + z^2(x + y)`
`= (x + y)[xy + z(x + y) + z^2]`
`= (x + y)[xy + xz + yz + z^2]`
`= (x + y)[x(y + z) + z(y + z)]`
`= (x + y)(y + z)(x + z).`
