𝑥^6 − 729
𝑥^6 − 729
According to the equation,
𝑎^3 − 𝑏^3 = (𝑎 − 𝑏)(𝑎^2 + 𝑎𝑏 + 𝑏^2)
So we get,
𝑥^6 − 729
= (𝑥^2)^3 − 9^3
Using the equation,
= (𝑥^2 − 9)((𝑥^2)^2 + (𝑥^2)(9) + 9^2)
= (𝑥^2 − 9)(𝑥^4 + 9𝑥^2 + 81)
Based on the equation,
= (𝑥 + 3)(𝑥 − 3)[(𝑥^2 + 9)^2 − (3𝑥)^2]
On further simplification
= (𝑥 + 3)(𝑥 − 3)(𝑥^2 + 9 + 3𝑥)(𝑥^2 + 9 − 3𝑥)
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