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Gauss, Ramanujan, and a pantheon of other mathematicians have given us algebraic manipulation tools way beyond what's taught in school. Learn what they knew.

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If \(a+b+c=1, a^2+b^2+c^2=11,\) and \(abc=2,\) what is the value of \[a^2b^2+b^2c^2+c^2a^2?\]

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If \(x^8 = 829\), what is \((x-1)(x+1)(x^2+1)(x^4+1)\)?

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