Evaluate
\frac{\left(2y-1\right)^{2}}{4}+\left(x-2\right)^{2}
Expand
x^{2}-4x+y^{2}-y+\frac{17}{4}
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x^{2}-4x+4+\left(y-\frac{1}{2}\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.
x^{2}-4x+4+y^{2}-y+\frac{1}{4}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-\frac{1}{2}\right)^{2}.
x^{2}-4x+\frac{17}{4}+y^{2}-y
Add 4 and \frac{1}{4} to get \frac{17}{4}.
x^{2}-4x+4+\left(y-\frac{1}{2}\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.
x^{2}-4x+4+y^{2}-y+\frac{1}{4}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-\frac{1}{2}\right)^{2}.
x^{2}-4x+\frac{17}{4}+y^{2}-y
Add 4 and \frac{1}{4} to get \frac{17}{4}.
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