Find the value of $(1 + w)^{3} - (1 + w^{2})^{3}$

0

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5

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Solution

The correct option is A $0$
$(1 + ω)^{3} - (1 + ω^{2})^{3} = (1 + ω - 1 - ω^{2}) [(1 + ω)^{2} + (1 + ω) (1 + ω^{2}) + (1 + ω^{2})^{2}] = (ω - ω^{2}) [1 + ω^{2} + 2 ω + 1 + ω^{2} + ω + ω^{3} + 1 + ω^{4} + 2 ω^{2}] = (ω - ω^{2}) [4 + 4 ω + 4 ω^{2}] = (ω - ω^{2}) \times 0 = 0$

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