<p>If (x+y)(x^2 - y^2) = 0, which of the following must be true?</p>
<p>A) x = y</p>
<p>B) x = -y</p>
<p>C) x^2 = y^2</p>
<p>D) x^2 = -y^2</p>
<p>E) x^3 = y^3</p>
<p>I had chosen x=-y as my answer, but it was apparently incorrect. The answer answer was C. Can someone please offer an explanation to why my answer was incorrect and why C is correct? I'm still not completely understanding CB's answer. </p>
<p>Thanks in advance!</p>
<p>Either A or B could be true, but only C must be true.</p>
<p>For example, x=5 and y=5 works (x=y). But so does x=5 and y=-5 (x=-y). In both cases, x^2 = y^2 = 25.</p>
<p>I don’t get this… Can’t a, b, and c all be true?</p>
<p>yes, but only c MUST be true. </p>
<p>For example, if x=2 and y=2, it satisfies the statement (the answer is 0) but b isn’t true. C is the only one that MUST be true.</p>
<p>A and B can be true but it’s not necessary that every time both variables fit that equation. When squared, the number will always be positive and therefore, equal to each other.</p>
<p>(x+y)(x^2-y^2)=0
divide both sides by (x+y) giving you x^2-y^2=0
then subtract y^2
Then you get: x^2=y^2</p>
<p>Since square roots can be +/- you can’t take square root and necessarily get x=y or x=-y</p>