Question

Hi, I need help to solve this problem. Just a note that the thought process and rules used in solving it will be appreciated. Problem is: u^2-2u+1-v^2

Answer 1

You basically have an equation in the form f(v^2, u^2). If you set v^2 off on one side of the equality, you would be able to factor "u" as a term squared.

Answer 2

If you leave the expression just as is, an expression, you can still express the first 3 terms as an expression in u, and it will be squared.

Answer 3

"u" and "v" can be thought of as "x" and "y" in a two-dimensional traditional Cartesian coordiante plane with a certain calculable center. This particular expression could be used as a part of a larger equation such as a circle.

Answer 4

Is there a name or pattern for this polynomial. Need to know how to recognize it and solve it next time.

Answer 5

As for solving or simplifying, think of u^2-2u+1-v^2 as (u^2 - 2u + 1) - v^2 and see if you can get the "u" into an expression of its own that is squared. Hint: think of "u - 1".

Answer 6

A good reference is the equation of a circle: (x - h)^2 + (y - k)^2 = r^2. You are not dealing with the exact same thing, but your expression could be used for an equation LIKE this.

Answer 7

THANK YOU VERY MUCH! I still need to give it more thought to understand why it is solved the way it is. Could you solve this with polynomial by grouping?

Answer 8

No, but that was good thinking to go through. You can't because there is no "v" in the 2u.

Answer 9

Okay. THANK YOU VERY MUCH FOR RESPONDING! monday

Answer 10

You're quite welcome!