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nth Term of A.P

Find the valu...

Question

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

125

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126

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128

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129

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Solution

The correct option is D $129$
$(2 + ω + ω^{2})^{3} - (1 - 3 ω + ω^{2}) - (1 - 3 ω + ω^{2})^{3} = 1^{3} - (1 + ω^{2} - 3 ω)^{3} - (1 + ω^{2} - 3 ω)^{3} 1 - (- ω - 3 ω)^{3} - (- ω - 3 ω)^{3} = 1 + (4 ω)^{3} + (4 ω)^{3} = 1 + 64 ω^{3} + 4 ω^{3} = 129$

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