We know the square of W + W = 1. Evaluation: the square of 1-w-w + the third power of W - the fourth power of W - the fifth power of W + the sixth power of W - the seventh power of W - the eighth power of W

We know the square of W + W = 1. Evaluation: the square of 1-w-w + the third power of W - the fourth power of W - the fifth power of W + the sixth power of W - the seventh power of W - the eighth power of W

Because the square of W + W = 1, so 1-w-w ^ 2 = 0
1-w-w's square + W's third power - W's fourth power - W's fifth power + W's sixth power - W's seventh power - W's eighth power
=1-w-w^2+w^3(1-w-w^2)+w^6(1-w-w^2)
=0+0+0=0