Hi! I came across this problem in one of the lecture videos and I was wondering why removing like terms does not work here. For example when you remove x from both sides, multiply out the left side, remove x^2 from both sides, you are left with -1 compared to 0 (in which case B is bigger). However, the answer is D.
In case the photo didn’t upload, the question is comparing A, which is (x-1)(x)(x+1) to B, which is (x)(x)(x).
If your definition of “removing like terms” involves dividing stuffs out, then it doesn’t work. That’s because you don’t know the signs of whatever you’re dividing out, which directly affects which quantity is greater.
Thanks! Greg tends to remove like terms a lot in these types of problems. In what situations can you add, subtract, divide, multiple like terms?
If in this case it was specified that x>0, could you remove like terms?
Adding and subtracting is fine, but you’d need to be cautious with dividing and multiplying.
Sure. In fact, if you’re careful with it (by handling different cases), you could start multiplying and dividing by negative numbers too — but it’s better to avoid the hassle altogether if you weren’t already doing so.
Also, if you really want to go the route of multiplying and dividing stuffs, then you can multiply both sides by \frac{1}{x^2} instead.
