SOLUTION: (x+y-2z)^2+2(x+y-2z)(x-2y+2z)+(x-2y+2z)^2

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Question 1041348: (x+y-2z)^2+2(x+y-2z)(x-2y+2z)+(x-2y+2z)^2
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

%28x%2By-2z%29%5E2%2B2%28x%2By-2z%29%28x-2y%2B2z%29%2B%28x-2y%2B2z%29%5E2

Let (x+y-2z) = p

Let (x-2y+2z) = q

Substituting,

p%5E2%2B2pq%2Bq%5E2

Factoring as a perfect square.

%28p%2Bq%29%5E2

Replacing p and q  with (x+y-2z) and (x-2y+2z),
respectively,

%28%28x%2By-2z%29%2B%28x-2y%2B2z%29%29%5E2

Removing parentheses,

%28x%2By-2z%2Bx-2y%2B2z%29%5E2

Collecting like terms,

%282x-y%29%5E2  

or multiplied out 

4x%5E2-4xy%2By%5E2

whichever of the last two forms you prefer.

Edwin