SOLUTION: By letting y=2-a, simplify the expression 〖(x+2-a)〗^2+〖(2-a-x)〗^2-2(x-2+a)(x+2-a)

Algebra ->  Finance -> SOLUTION: By letting y=2-a, simplify the expression 〖(x+2-a)〗^2+〖(2-a-x)〗^2-2(x-2+a)(x+2-a)       Log On


   

Question 1198895: By letting y=2-a, simplify the expression
〖(x+2-a)〗^2+〖(2-a-x)〗^2-2(x-2+a)(x+2-a)
Found 2 solutions by greenestamps, MathLover1:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


%28%28x%2B2-a%29%29%5E2%2B%28%282-a-x%29%29%5E2-2%28x-2%2Ba%29%28x%2B2-a%29

Define y = 2-a

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

Now define m = x+y and n = x-y

m%5E2%2Bn%5E2-2mn+=+m%5E2-2mn%2Bn%5E2+=+%28m-n%29%5E2

Now go back and replace m, n, and y with their equivalent expressions

%28m-n%29%5E2=%28%28x%2By%29-%28x-y%29%29%5E2=%282y%29%5E2+=+4y%5E2=4%282-a%29%5E2

ANSWER: 4(2-a)^2 or, equivalently, 4(a-2)^2

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Given:



By letting y=2-a, simplify the expression
%28x%2B2-a%29%5E2%2B%282-a-x%29%5E2-2%28x-2%2Ba%29%28x%2B2-a%29

if y=2-a,then
%28x%2B2-a%29%5E2%2B%282-a-x%29%5E2-2%28x-%282-a%29%29%28x%2B2-a%29
%28x%2By%29%5E2%2B%28y-x%29%5E2-2%28x-y%29%28x%2By%29
x%5E2+%2B+2+x+y+%2B+y%5E2%2Bx%5E2+-+2+x+y+%2B+y%5E2-2%28x%5E2+-+y%5E2%29
x%5E2+%2B+2+x+y+%2B+y%5E2%2Bx%5E2+-+2+x+y+%2B+y%5E2-2x%5E2+%2B2y%5E2
2x%5E2+%2B+2+x+y++-+2+x+y+-2x%5E2+%2B4y%5E2
cross%282x%5E2%29+%2B+cross%282+x+y%29++-cross%282+x+y%29+-cross%282x%5E2%29+%2B4y%5E2
4y%5E2

go back and replace y with 2-a

4%282-a%29%5E2=>answer