<p>I can do this problem but it would take a pretty long time. My method was just to subsitute and expand. I expanded I and II to see if they work but ran out of time so I could not finish the problem.</p>
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<p>I wouldn’t write it out. I don’t think there is a better way than just making x,y,z=1 and expanding in your head.</p>
<p>ohhh, just sub 1 for each variable…that would make it alot easier. dam im dumb haha. thanks</p>
<p>You wrote too much bro. You should have just substituted on your calculator and just wrote down the final answer of each part of the equality. Then in the end, decide if they are equal. I barely write in the SAT btw, whether that be English, Writing or Maths. You don’t get extra points. You don’t get anything out of it, they don’t even look at those papers as a matter of fact. It’s completely useless. Cut it, and value your precious time.</p>
<p>Substituting x=y=z=1 is useful only to eliminate options. If an identity tests out it does not mean that it is true for all values of the variables.</p>
<p>The correct way to do this is as you were doing it. You can quickly eliminate option III when you expand. Option I is obviously true since both sides of the definition are symmetric in a and b (you can interchange them and the identify holds). The only question then is II. You can quickly expand both sides to validate it.</p>
<p>I’m not sure I understand why you ran out of time.</p>
<p>Not to mention that this is supposed to be the hardest question in the section. Notice number “20.” That means, you should have about 5-10 minutes saved up for this question, in which it would only take 2-3 minutes had you not written so much, and simply transferred the writing to your calculator.</p>
<p>There is nothing wrong with making up #s here. But I would not have used all 1’s. They ask which MUST be true. 1 is an unusal number. Lots of things are true about 1 that are not always true. Also, I would not have used the same number for all three…</p>
<p>Sorry guys, I’m not a very fast expander.</p>
<p>Thank you for the multiple explanations! I too would never assign the same number to all 3 variables especially not 1 which is way too risky. I should have assigned numbers though such as 2,4,6.</p>
<p>For the advanced student only:</p>
<p>You can figure this out fairly quickly if you understand the basic laws of commutativity and distributivity.</p>
<p>I is true because addition and multiplication are both commutative (no need to write anything)</p>
<p>III is false. Here’s how you can see this very quickly. Since multiplication distributes over addition you can disregard “ab” (because it will come out the same on both sides). For the rest, the left becomes x+y+z, and the right becomes x+y+x+z. These are clearly not always equal.</p>
<p>II you should write out in detail. To save time, note that (x-1)(x+1) is the factored form of the difference of 2 squares, so is equal to x^2-1 (equivalently, when you multiply conjugates the inners and outers always cancel, so you just need to do first and last).</p>
<p>Remark: I am not necessarily recommending that you do things this way on the SAT itself, but having a deeper understanding as presented here will increase your level of mathematical maturity, and this will increase the likelihood of you scoring an 800.</p>
