Then, Which line is the first that contains an error in this proof?
Let's consider the transition from line 1 to 2: is subtracted from both sides of the equal sign. Is it equally valid to do the operation below instead?
On the left-hand side of line 3, the value is "factored out" from to get
Is the equation below true?
Changing to is known as the difference of squares identity (it was first introduced in a previous course, as shown in the video below). What if we started with fourth powers instead, that is, Which expression is equivalent?
Let's go back to the moment of mistake: does what is known as a "cancel" on both sides of the equal sign. Since the problem set up this implies division by zero. Suppose that instead; what identity would be used to cancel? Assume