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