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$(a + b)^2 = a^2 + 2ab + b^2$, so $a^2 + b^2 = (a + b)^2 - 2ab$. Also $x^3 + \frac{1}{x^3} = \left(x + \frac{1}{x}\right)^3 - 3\left(x + \frac{1}{x}\right)$.
Algebraic identities
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