Is y=x the same thing as y^2=x^2 and why?

Question

But (-1)^2 is 1.

Answer 1

Yes, because if y = x, then y*y = x*x.  If y and x are the same, when you square them they will still be the same.  It's difficult to explain any other way.  Just try it with any example:

Example: 2+1 = 3

(2 + 1)^2 = 3^2

(2+1)(2+1) = 3^2

4 + 2 + 2 + 1 = 3^2

9 = 3^2 = 9

Answer 2

no it is not the same

y^2 = x^2 is the same as y = the absolute value of x

Answer 3

No, they are not the same.

Here's an example.

(-1)² = (1)²

But -1 does not equal 1.

Answer 4

It's not the same. Why? Because, your first statement says positive x is equal to positive y; in the second statement, y and x could be negative (a negative number squared is positive). If you look at the second statement as an equation and square root the whole thing, you'll get plus or minus y= plus or minus x ( the plus or minus is introduced when you square root). This is if both statements are independent of each other.

In the case where they are dependent on each other (like someone tells you y=x as a fact, and then asks you if y^2=x^2 is true), then yeah, these would be equivalent, because you squared both sides of the first statement.  I hope this helps :)