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x^{2}-y^{2}-2y
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x^{2}-y^{2}-2y
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x^{2}-2xy+y^{2}-2y\left(y-x+1\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-y\right)^{2}.
x^{2}-2xy+y^{2}-2y^{2}+2yx-2y
Use the distributive property to multiply -2y by y-x+1.
x^{2}-2xy-y^{2}+2yx-2y
Combine y^{2} and -2y^{2} to get -y^{2}.
x^{2}-y^{2}-2y
Combine -2xy and 2yx to get 0.
x^{2}-2xy+y^{2}-2y\left(y-x+1\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-y\right)^{2}.
x^{2}-2xy+y^{2}-2y^{2}+2yx-2y
Use the distributive property to multiply -2y by y-x+1.
x^{2}-2xy-y^{2}+2yx-2y
Combine y^{2} and -2y^{2} to get -y^{2}.
x^{2}-y^{2}-2y
Combine -2xy and 2yx to get 0.
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Limits
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