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Question Number 46168 by peter frank last updated on 21/Oct/18

Answered by tanmay.chaudhury50@gmail.com last updated on 22/Oct/18

1+w+w^2 =0 w^3 =1 1)(−w^2 −w^2 )^3 −(−w−w)^3 =(−2w^2 )^3 −(−2w)^3 =−8(w^3 )^2 +8w^3 =−8+8=0

1+w+w2=0w3=11)(−w2−w2)3−(−w−w)3=(−2w2)3−(−2w)3=−8(w3)2+8w3=−8+8=0

Answered by tanmay.chaudhury50@gmail.com last updated on 22/Oct/18

2)a^2 +abw^2 +acw+abw+b^2 w^3 +bcw^2 +acw^2 +bcw^4 +c^2 w^3 =a^2 +b^2 +c^2 +ab(w^2 +w)+bc(w^2 +w^3 .w)+ac(w+w^2 ) =a^2 +b^2 +c^2 −ab−bc−ac

2)a2+abw2+acw+abw+b2w3+bcw2+acw2+bcw4+c2w3=a2+b2+c2+ab(w2+w)+bc(w2+w3.w)+ac(w+w2)=a2+b2+c2−ab−bc−ac

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