+64 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 $x^2 + y^2?$
+1946 First, let's expand (x+y)2 and see what we get.
We have (x+y)2=x2+2xy+y2 as our full expansion.
Setting (x+y)2=x2+y2, we have the equation
x2+2xy+y2=x2+y2. Cancelling out terms, we get that
2xy=0xy=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! :)
