𝑎^3 -1/𝑎^3 − 2𝑎 +2/𝑎
𝑎^3 -1/𝑎^3 − 2𝑎 +2/𝑎
= 𝑎^3 −1/𝑎^3 − 2(𝑎 −1/𝑎)
According to the equation,
𝑎^3 − 𝑏^3 = (𝑎 − 𝑏)(𝑎^2 + 𝑎𝑏 + 𝑏^2)
So we get,
𝑎^3 −1/𝑎^3 − 2(𝑎 +1/𝑎)
= (𝑎 −1/𝑎)(𝑎^2 + 𝑎(1/𝑎) + (1/𝑎)^2) − 2(𝑎 −1/𝑎)
On further simplification
= (𝑎 −1/𝑎)(𝑎^2 + 1 +1/𝑎^2 − 2)
= (𝑎 −1/𝑎)(𝑎^2 +1/𝑎^2 − 1)
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