Maths Olympiad Prep

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, 2014

Algebra Difficulty 1.4 Junior Find the answer Canada

If x=2yx=2y and y0y \neq 0, then (xy)(2x+y)(x-y)(2x+y) equals

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Solution

Since x=2yx=2y, then (xy)(2x+y)=(2yy)(2(2y)+y)=(y)(5y)=5y2(x-y)(2x+y)=(2y-y)(2(2y)+y)=(y)(5y) = 5y^2.

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