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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 \(-x^3+6x^2-6x+36\) is factorized as \((a-x)(x^2+b),\) what is the value of \(a+b\)?

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If \(x+2y-6+3(1-x-2y)=-51\), what is \(x+2y\)?

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If \(x+2y=-13\), what is the value of \[x^2+4xy-2x-4y-3+4y^2?\]

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