Chapter 11.5, Problem 1AYU

True or False The equation ${\left(x-1\right)}^2-1=x\left(x-2\right)$ is an example of an identity. (p. A43)

To determine

True or False.

Answer to Problem 1AYU

Solution:

True.

Explanation of Solution

Given:

${\left(x - 1\right)}^2 - 1 = x\left(x - 2\right)$ is an example of identity.

$\begin{array}{llll}\text{Consider} \text{LHS}:\hfill & {(x - 1)}^2 - 1\hfill & = \hfill & x^2 + 1 - 2x - 1\hfill \\ \hfill & \hfill & = \hfill & x^2 - 2x\hfill \\ \hfill & \hfill & = \hfill & x(x - 2)\hfill \\ \hfill & \hfill & = \hfill & \text{RHS}\hfill \end{array}$

Hence, ${\left(x - 1\right)}^2 - 1 = x\left(x - 2\right)$ is an example of $\text{identity} - \text{True}$.