Maths Olympiad Prep

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, 2014

Algebra Difficulty 1.1 Junior Find the answer Canada

If x=2x=2, then (x+2x)(2x2)(x+2-x)(2-x-2) equals

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Solution

When x=2x=2, we have (x+2x)(2x2)=(2+22)(222)=(2)(2)=4(x+2-x)(2-x-2)=(2+2-2)(2-2-2)=(2)(-2)=-4.

Alternatively, we could simplify (x+2x)(2x2)(x+2-x)(2-x-2) to obtain (2)(x)(2)(-x) or 2x-2x and then substitute x=2x=2 to obtain a result of 2(2)-2(2) or 4-4.

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.