1. Expand and simplify

Question

a) (2-x)^-2
b) (2+x)^-2
c) General formula for
i) (x+y)^-n
ii) (x-y)^-n
iii) (x+y)^1/n
iv) (x+y)^n/m
v) (x+y)^-1/n
vi) (x+y)^-n/m
vii) (x-y)^1/n
viii) (x-y)^n/m
ix) (x-y)^-1/n
x) (x-y)^-n/m
Using Binomial theory and combination respectively
2. Write the Paschal Triangle for
a) (2-x)^-2
b) (2+x)^-2
c) General formula for
i) (x+y)^-n
ii) (x-y)^-n
iii) (x+y)^1/n
iv) (x+y)^n/m
v) (x+y)^-1/n
vi) (x+y)^-n/m
vii) (x-y)^1/n
viii) (x-y)^n/m
ix) (x-y)^-1/n
x) (x-y)^-n/m?

Answer 1

Where did you get stuck?

Answer 2

all of these just use the binomial theorem:

(a+b)^n = nC0 a^n b^0 + nC1 a^(n-1) b^1 + ... + nCk a^(n-k) b^k + ...