Maths Olympiad Prep

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, 2014

Algebra Difficulty 2.5 Junior Find the answer Canada

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

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Solution

We simplify first, then substitute x=2yx=2y: (x+2y)(2x+y)=x+2y2xy=yx=y2y=y(x+2y)-(2x+y)=x+2y-2x-y=y-x = y - 2y = -y Alternatively, we could substitute first, then simplify: (x+2y)(2x+y)=(2y+2y)(2(2y)+y)=4y5y=y(x+2y)-(2x+y)=(2y+2y)-(2(2y)+y) = 4y - 5y = -y

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