Difference in expansion of brackets

[mathlearn]

Let's say that there is an expression $x^2+y^2=14$

Cannot this expression be written as $(x+y)^2 = 14$ taking out the square which is common to both the terms $x$ and $y$ but after writing like that doesn't this become $x^2+2xy+y^2$=14

So writing the expression like that would it remain valid or not ?

 

[MarkFL]

In general, we have:

$$(a+b)^2\ne a^2+b^2$$

Students make this mistake so often it has been given a name...The Freshman's Dream.