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From profit/cost models to the flight of a baseball to approximating the motion of a wave, polynomials are a mathematical way to represent values which are sums of powers of variables.

If \(x^2=7\), what is the value of \[(x+3)^3-(x-3)^3?\]

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Simplify

\[ ( 2 + \sqrt{3})^3 + ( 2 - \sqrt{3})^3. \]

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If \[8x^3-512y^3=(2x-ay)(bx^2+cxy+dy^2),\] what is the value of \(a+b+c+d\)?

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Simplify

\[ ( 4 + \sqrt{19})^3 + ( 4 - \sqrt{19})^3. \]

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If \[x^3+8=(x+a)(x^2+bx+c),\] what is the value of \(a+b+c\)?

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