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Algebra Difficulty 1.9 Junior Find the answer

If x=2yx=2y and y0y \neq 0, what is the value of (x+2y)(2x+y)(x+2y)-(2x+y)?

A number or a short expression. Spacing and $ signs are ignored.

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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