(2𝑎 + 1)^3 + (𝑎 − 1)^3
(2𝑎 + 1)^3 + (𝑎 − 1)^3
According to the equation
𝑎^3 + 𝑏^3 = (𝑎 + 𝑏)(𝑎^2 − 𝑎𝑏 + 𝑏^2)
We get,
= ((2𝑎 + 1) + (𝑎 − 1))((2𝑎 + 1)^2 − (2𝑎 + 1)(𝑎 − 1) + (𝑎 − 1)^2)
According to the equation,
(𝑎 + 𝑏)^2 = 𝑎^2 + 2𝑎𝑏 + 𝑏^2
(𝑎 − 𝑏)^2 = 𝑎^2 − 2𝑎𝑏 + 𝑏^2
So we get,
= (2𝑎 + 1 + 𝑎 − 1)( (2𝑎)^2 + 2(2𝑎)(1) + 1^2 − 2𝑎^2 + 2𝑎 − 𝑎 + 1 + 𝑎^2 − 2𝑎(1) + 1^2)
= 3𝑎(4𝑎^2 + 4𝑎 + 1 − 2𝑎^2 + 𝑎 + 1 + 𝑎^2 − 2𝑎 + 1)
= 3𝑎(3𝑎^2 + 3𝑎 + 3)
By taking 3 as common
= 9𝑎(𝑎^2 + 𝑎 + 1)
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