1. The problem is to simplify the expression $$(x-\frac{\alpha}{\beta})(x-\frac{\alpha}{\beta}).$$ 2. Recognize that this is a product of two identical binomials, so it can be rewritten as a square: $$\left(x-\frac{\alpha}{\beta}\right)^2$$ 3. Expand the square using the formula $$(a-b)^2 = a^2 - 2ab + b^2$$ where $$a=x$$ and $$b=\frac{\alpha}{\beta}$$: $$x^2 - 2x \cdot \frac{\alpha}{\beta} + \left(\frac{\alpha}{\beta}\right)^2$$ 4. Simplify the middle term: $$-2x \cdot \frac{\alpha}{\beta} = -\frac{2\alpha}{\beta}x$$ 5. Write the final expanded and simplified expression: $$x^2 - \frac{2\alpha}{\beta}x + \frac{\alpha^2}{\beta^2}$$