1 and 2. There's no way. Turn them into improper fractions. Well, the process would be a lot faster if you notice the relationship between 2 2/5 and /12. But basically, it's improper-ization, and reduction.
4. The expansion of a binomial to the nth power has n+1 terms
5. Memorize your pascal triangle. On the "5" roll it's 1,5,10,10,5,1. And the x's power on that term is 2 and y's is 3 so it's 10*(2^2)*(-1^3) = -400. The key is to notice the relationship btw Pascal triangle and the coefficients of expansions of binomial to different powers.
(5) the simplified coefficiant of the 4th term in the expansion of (2x-y)^5:
Another way to do this problem (rather than memorizing Pascal's triangle coefficients) is to use combinations:
5C(4-1)
In this case the exponent is 5 and the nth term is 4, so take the combination of 5 items (4-1) or 3 at a time. This equals 10 which is the same as you get using Pascal's triangle. Then multiply this times the square of the (2) coefficient times the cube of the (-1) coefficient (because the 4th term is x2y3) to get your answer (which should be -40).
