Know any other ways apart from bionomial xpansion trialerror? (1 Viewer)

[AndyDandy]

answer is C

 

[jimmysmith560]

If you are looking for a non-zero constant term, you are essentially looking for where the x's cancel out. Considering the first term of option A, you would have x7. The next term would have the coefficient multiplied by x6 multiplied by 1/x^2. This equates to the coefficient by x4. The logic here is that by lowering the power of x by one, and increasing the power of 1/x^2 by one, you are effectively making the 'power differential' 3. So you would get down to x^4, then x^1, and so on in an arithmetic series until the last term.

The same logic applies to the other options. For B, you start with the first term x^14, and count the powers down by fives (because 2+3=5). For C, you start with first term x^21, and count down by sevens. This will get to an x^0 term, and therefore (C) is the answer.

I hope this helps!

 

[5uckerberg]

View attachment 33805answer is C

A very easy way to work this question out is by replacing the terms with , next step is to start from the basics as in and as one can see it becomes for your case it can we written for each of the terms it can be written as find the one that gives an integer value of r and there you are done. Note this is a common 2-3 marker question.

What I mean is this a 2 marker question would involve one to find the coefficient for a particular term or finding a constant term.
A 3 marker question would make you find the greatest coefficient and as such requires you to write .
Another possible type of question that is a 2 marker would be the binomial theorem and they want you to do all sorts of things with it could be differentiating or say let x=1 as such which you could get or whatever power.

To summarise there are too many different avenues for this topic. You can combine this with the topic of probability and make it an interesting question for candidates to encounter.