Question

Simplify the expression. $$(\sqrt{a}-b)^{2}$$

Short answer

The simplified form of the expression \((\sqrt{a}-b)^{2}\) is \(a - 2 * \sqrt{a} * b + b^{2}\).

Step-by-step solution

Understanding the problem

The expression \((\sqrt{a}-b)^{2}\) needs to be simplified. This is equivalent to the square of the binomial expression \(\sqrt{a}-b\). Use the expansion of \((a-b)^{2}\) to simplify.

Apply the formula of square of binomial

The square of a difference, or \((a-b)^{2}\), is equal to \(a^{2}-2ab+b^{2}\). Applying this formula to our expression where \(a = \sqrt{a}\) and \(b = b\), we get \((\sqrt{a})^{2}-2*\sqrt{a}*b+b^{2}\).

Simplify further

The \((\sqrt{a})^{2}\) leads to \(a\), because the square root and the square operations cancel each other out. So, the result is \(a - 2 * \sqrt{a} * b + b^{2}\).