In this video, Achievable GRE course author Matt Roy explains how FOIL to simplify an expression. He also teaches a shortcut that allows you to do the problem in 10% of the time!
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00:00:03 In this question we just have a quadratic that needs to be simplified. So the first thing you need to do is write it out twice. So we have sqrt 16 X minus sqrt X * sqrt 16 X minus the square root of X. Now in order to foil you just need to multiply it first times, first outside, outside, inside, inside, and last last. 00:00:28 So first times first is sqrt 16 X times itself. Now the square root of anything times itself is just simply what is written inside of the house or the square root symbol. So that just means that that equals 16X. Think about sqrt. 25 is five, and that times itself is 25, so sqrt 25 times itself is just 25. All right, so. 00:00:58 Now we have to do outside and inside. So outside is sqrt 16 X times negative. The square root of X. Well, that will become negative anything. So we have negative times sqrt 16 X squared. Because with radicals if you multiply you can put it all together into the same place. So we have 16 * X ^2. Sqrt 16 is 4 sqrt X ^2 is X. 00:01:27 So we just have -. 4 X. Now inside is actually the same as outside 16 or sqrt. 16 X times negative. The square root of negative square root of X. Again and again that would be - 4 X. So the inside and the outside combines to -, 8 X. So we start off with 16X, negative 8X and then last times last is the negative square root of X. 00:01:56 Times negative, square root of X negative times a negative is a positive squared of anything times itself. Again, is just what is written inside of the radical symbol, which is X. So we have a + X at the end. This leaves us with a total of 9X. Now there is one way to do this question really simply if you were to imagine any number for X. 00:02:24 Let's just say you plug in one for X. We can solve for what this expression must be plugging in X and determine which answer equals that given our value of X. So for example, if we just plug in one, we get sqrt 16 for the first part that is 4. And then obviously sqrt 1 is 1, so we have 4 -, 1, which is 3 squared. That's nine. 00:02:52 Lugging in the number we have chosen for X into all of the answers, only nine X = 9, so that's the answer.
