(A) To expand the expression $(x - \frac{1}{2})^{2}$,we use the algebraic identity $(a - b)^{2} = a^{2} - 2ab + b^{2}$.Here,$a = x$ and $b = \frac{1}{

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(A) To expand the expression $(x - \frac{1}{2})^{2}$,we use the algebraic identity $(a - b)^{2} = a^{2} - 2ab + b^{2}$.Here,$a = x$ and $b = \frac{1}{2}$.Substituting these values into the identity:$(x - \frac{1}{2})^{2} = (x)^{2} - 2(x)(\frac{1}{2}) + (\frac{1}{2})^{2}$.Simplifying the terms:$= x^{2} - x + \frac{1}{4}$.