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Question

Evaluate (x+α)(x+β)(αγ)(βγ)+(x+β)(x+γ)(βα)(γα)+(x+α)(x+γ)(γβ)(αβ)=?

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Solution

Now,
(x+α)(x+β)(αγ)(βγ)+(x+β)(x+γ)(βα)(γα)+(x+α)(x+γ)(γβ)(αβ)
x2+x(α+β)+α.β(αγ)(βγ)+x2+x(β+γ)+β.γ(βα)(γα)+x2+x(α+γ)+α.γ(γβ)(αβ)
={x2[(βα)+(γβ)+(αγ)]+x[(β2α2)+(γ2α2)+(α2γ2)]+[α.β(βα)+β.γ(β+γ)+γ.α(αγ)]}(αβ)(βγ)(γα))
={[α.β(βα)+β.γ(β+γ)+γ.α(αγ)]}(αβ)(βγ)(γα))

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