<p>If (x + y)(x^2 - y^2) = 0, which of the following must be true?</p>
<p>(A) x = y
(B) x = -y
(C) x^2 = y^2
(D) x^2 = -y^2
(E) x^3 = y^3</p>
<p>Please explain your answer. </p>
<p>Thanks.</p>
<p>(b) is the correct answer. For the equation to be true, either (x+y) or (x^2 - y^2) has to equal 0. So, set either one equal to 0. I’d prefer to solve x+y=0 simply because it’s easier to solve.</p>
<p>x+y=0–>x=-y–>(B)</p>
<p>It should be C, x^2 = y^2. If you solve for x using the first one (x+y) you get x = -y. But, you also have to set x^2 - y^2 equal to zero and you get x^2 = y^2, which will give you x = y or -y when you square root it. So only C is correct.</p>
<p>The answer is indeed C, and thank you very much Apoc314. That makes sense.</p>
<p>But, if one of the two (either x+y or x^2-y^2) is zero, the entire thing will equal zero. So if x=-y, (x + y)(x^2 - y^2) will equal (-y + y)(x^2 - y^2) which equals (0)(x^2 - y^2)=0.</p>
<p>EDIT: The method I used above eliminates half of the possible answers. It should be (C). Sorry, I’ve been off my game recently.</p>