Question

True or False The equation${(x-1)}^2-1=x(x-2)$ is an example of an identity

Short answer

The given statement is true.

Step-by-step solution

Step 1. Given data

The given equation is ${(x-1)}^2-1=x(x-2)$

Here, the left-hand side equation can be written aslocalid="1647456931703" ${(x-1)}^2-1^2$.

This is in the form of localid="1647517093435" $A^2-B^2$

We know the identity$A^2-B^2=(A+B)(A-B)$$A^2-B^2=(A+B)(A-B)$

Step 2. Expand the equation using identity

$$\begin{gathered} (x-1{)}^2-1^2=(x-1+1)(x-1-1) \\ =x(x-2) \end{gathered}$$

Therefore, this equation is an example of identity.

Hence, the given statement is true.