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(1-w) (1-w^2) (1-w^4) (1-w^8) = ? (a) 16 (b) 8 (c) 9 (d) 64

(1-w) (1-w^2) (1-w^4) (1-w^8) = ? (a) 16 (b) 8 (c) 9 (d) 64

Grade:12th pass

1 Answers

nitish
36 Points
7 years ago
see if u know that w^4=w   (as w^3=1)
and w^8=w^2
the given expression can be reduced to (1-w)^2*(1-w^2)^2
now try expanding this expression you get:1+w- 2w^2+w^2+1-2w-2w+4-2w^2
now this can be simplified to 6-3w-3w^2         (as 1+w+w^2=0)
6-3(w+w^2)=6+3=9
so the final answer is 9.

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