Maths help!! PLEASE?

Question

Maths ( 2 questions ) Easy Questions I need help! not easy for me ..?
Math Problems Please?
Hey, everyone these questions are due on wednesday, and ive done most of the sheet and i just have these questions left. Could someone please answer with full solutions. thank you so much in advance, and help will be appreciated, as the questions have been hard for me to solve and i really would like to know, how it should be done. Thank You..
Question 14) Expand the following using the binomial theorem:
c) (x+y)^6

h) (1+x)^5

j) (1-x)^4

l) (1-x)^6

m) (1-2x)^5

n) (2/a - a)^4

o) (x-2/x)^4

p) (2x+3y)^4

q) (x-2y)^5

r) (2a-b)^4

s) (x+1/x)^5

t) (x^2-2/x^2)^4

u) (1-x/2)^5

Question 17) Find the coefficient of:
a) x in (3x^2 + 2/x)^5

b) x in (x-2^x-1)^5

c) x^3 in (x-2/x)^7

d) x^3 in (x-1/2x)^9

e) x^4 in (x-1/2x)^10

f) p^4q^2 in (p+q)^6

g) x^5 in (1+2x)^7

h) x^3 in (2x-2)^10

i) x^5 in (x - 2/ x^2)^11

j) x^5 in (x+1/x)^9

Answer 1

I dont know if you have learned about Pascal's Triangle but that is the easiest wat to do what you are doing

here is pascal's triangle

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1

and so on

(sorry about the formatting if you go on to this web site you will see what it actually looks like in triangle form http://www.krysstal.com/binomial.html)

I will show you how to do this question and then you can do the rest

expand (1+x)^5

that would be

x^5+5(x^4*y)+10(x^3*y^2)+10(x^2*y^3)+5(x*y^4)+1(y^5)

now you should notice that the numeric coefficients are the numbers from the 5th line of pascal's triangle and the exponents of the letters in the brackets start a 5 and go down to 0 for X and start at 0 and go up to 5 for Y

I hope this helps you do the rest of the questions