Find the middle term .. (2p - ½q )^10

how do we get the coefficient for the each term? well, the first coefficient is 1, and all subsequents are "the product of the current coefficient and the exponent of the first element divided by the exponent of the second element on the next term", so, that's a mouthful, but for example,

for the 5th term of the expansion, how did we get 210?  well, is just 120 * 7 / 4.

for the 6th term, how did we get 252?  well, is just 210 * 6 / 5.

recall that if the exponent is 10, that means the expansion will be 11 terms, and therefore the middle term will be the 6th one.

so, just combine the 6th term away.

First, think of what you know. you know that the number t the end of the equation will need to be subtracted because it is the money he lost from buying the lawn mower. and your first two weeks have negative profit, so that tells you that c and d are wrong. now you can plug any of the weeks into a and b to see which one works. i'll start with plugging week 1 into a.this isn't right because it says your answer for week one should be -90.so now we need to try the same thing with b.this one got you the right answer, (sometimes if you only check with one of the weeks multiple will work so you need to check with more of the weeks, but it worked out fine here)this means that b is the correct answer.let me know if you need more clarification. i hope this : )