Question

Find the expression that represents the length of the hypotenuse of a right triangle whose legs measure m^2-n^2 and 2mn

Answer 1

(side 1)^2 + (side 2)^2 = hyp^2
 [m^2-n^2]^2  +  [2mn]^ = hyp^2

Then 

  m^4 - 2m^2n^2 + n^4 + 4m^2n^2 = hyp^2

m^4 + 2m^2n^2 + n^4 = hyp^2

Then hyp = +sqrt(m^4 + 2m^2n^2 + n^4) = +(m^2 + n^2)   (answer)