posted by Justin on .
I have a problem that states to simplify.
The equation is d=sqrt(x^2+(4-x^2-2)^2)
The book tells me that the answer simplifies to sqrt(x^4-3x^2+4).
Can you please help me understand where the -3x^2 came from?
d=√(x^2 + (4 - x^2 - 2)^2)
=√(x^2 + (2 - x^2)^2)
=√(x^2 + x^4 - 4x^2 + 4)
=√(x^4 - 3x^2 + 4)
In my opinion, this is not much of a "simplification" problem
(4-x^2-2)^2 = (2 - x^2)^2 = x^4 - 4x^2 + 4
When you add the x^2 to that, you get
x^4 - 3x^2 + 4
(4 - x^2 - 2)^2 simplifies to (2 - x^2)^2. Expanding it gives x^4 - 2x^2 - 2x^2 + 4 = x^4 - 4x^4 + 4. Then you have that x^2 out in front that you can work with. so x^4 + x^2 - 4x^2 + 4 = x^4 - 3x^2 + 4.