Question 895124: how to answer
(p-q)^2+(q-p)^2
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! (p-q)^2+(q-p)^2
since q-p = -(p-q), this becomes equal to:
(p-q)^2 + (-(p-q))^2 which becomes equal to (p-q)^2 + (p-q)^2 = 2*(p-q)^2
if you expand both of these, you will see that the solution for each is exactly the same.
(p-q)^2 = p^2 - 2pq + q^2
(q-p)^2 = q^2 - 2pq + p^2
rearrange the terms and the results are the same for both.
p^2 - 2pq + q^2 is the same as q^2 - 2pq + p^2.
q-p is the negative of p-q.
if you square the positive you get a positive.
if you square the negative you get a positive.
this might be easier to see with numbers.
let p = 5 and q = 3
p-q = 2
q-p = -2
2^2 = 4 and (-2)^2 = 4
since the power of the exponent is even, the result will be positive regardless if the argument is negative or positive.
|
|
|
