Maths Olympiad Prep

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, 2016

Algebra Difficulty 1.0 Junior Prove it United Kingdom

(a) Expand and simplify (ab)(a2+ab+b2)(a - b)(a^2 + ab + b^2).

(b) Find the value of 20163+201532016220152.\dfrac{2016^3 + 2015^3}{2016^2 - 2015^2}.

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Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.