+60 b) For which values of x and y does $(x + y)^2$ equal $x^2 + y^2?$ For which values of x and y does $(x + y)^2$ not equal $x^2 + y^2?$
+1876 First, let's expand \((x+y)^2\) and see what we get.
We have \((x+y)^2 = x^2+2xy+y^2\) as our full expansion.
Setting \((x + y)^2=x^2 + y^2\), we have the equation
\(x^2+2xy+y^2 = x^2+y^2\). Cancelling out terms, we get that
\(2xy=0\\ xy=0\)
So we must have xy=0, in order for it to be possible.
This means either x or y must be 0 for this to happen. If neither are 0, then we have the equation at false.
So our answer is \(xy=0\)
Thanks! :)
