Chapter A.10, Problem 35AYU

To determine

To find: Simplify the expression ${(\sqrt{x}-1)}^2$.

Answer to Problem 35AYU

The value of ${(\sqrt{x}-1)}^2=x+1-2\sqrt{x}$.

Explanation of Solution

Given:

It is asked to find the simplest form of the given expression ${(\sqrt{x}-1)}^2$.

Calculation:

Consider ${(\sqrt{x}-1)}^2$,

$(\sqrt{x}-1{)}^2=(\sqrt{x}{)}^2+1-2\sqrt{x}$

$=\left|x\right|+1-2\sqrt{x}=x+1-2\sqrt{x}$