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Polynomials & Rational Functions

Review question

Can we factorise $a^3(b-c)+b^3(c-a)+c^3(a-b)$?
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Ref: R7991

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Suggestion

Prove that \[\frac{1}{(2-\sqrt{3})^3}+\frac{1}{(2+\sqrt{3})^3}=52.\]

Could we write these two fractions as a single fraction?

What happens if we expand \((a+b)^3 + (a-b)^3?\)