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X²+2xy+y²=?

1 Answer

Jun 13, 2018

$x^{2} + 2 x y + y^{2} = {(x + y)}^{2}$ $x^2+2xy+y^2 = (x+y)^2$

Explanation:

It is not exactly clear what the questioner had in mind here.
I will assume we are to simplify the expression (and that $X = x$ $X=x$ )

$f (x, y) = x^{2} + 2 x y + y^{2}$ $f(x,y) = x^2+2xy+y^2$

$f (x, y)$ $f(x,y)$ is the well known expansion of ${(x + y)}^{2}$ $(x+y)^2$

Check: $(x + y) (x + y) = x^{2} + x y + y x + y^{2}$ $(x+y)(x+y) = x^2 + xy +yx +y^2$

$= x^{2} + 2 x y + y^{2}$ $= x^2+2xy+y^2$

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