If `f(x+2y , x-2y)=x y ,` then `f(x,y)` equals

Explanation

`f(x+2y,x-2y) = xy`

Let `x+2y = a ->(1)`

Let `x-2y = b ->(2)`

Adding `(1)` and `(2)`,

`x+2y+x-2y = a+b => x = (a+b)/2`

Subtracting `(1) - (2)`,

`x+2y-x+2y = a-b => y = (a-b)/4`

`:. f(a,b) = ((a+b)/2)((a-b)/4) = (a^2-b^2)/8`

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