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x^{2}+xy+\frac{1}{4}y^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+\frac{1}{2}y\right)^{2}.
x^{2}+xy+\frac{1}{4}y^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+\frac{1}{2}y\right)^{2}.