Exit fullscreen mode

Polynomials & Rational Functions

Review question

Can we factorise $a^3(b-c)+b^3(c-a)+c^3(a-b)$?
Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R7991

Printable/supporting materials Printable version Fullscreen mode Teacher notes

Question

Prove that \[\frac{1}{(2-\sqrt{3})^3}+\frac{1}{(2+\sqrt{3})^3}=52.\]
Show that \((a-b)\) is a factor of \[a^3(b-c)+b^3(c-a)+c^3(a-b)\] and hence factorise the expression completely.