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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 $x^2 + y^2?$

 Jun 18, 2024
 #2
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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! :)

 Jun 18, 2024

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