Question

simplify: (x+y)^10

simplify: (2a+5)^5

Answer 1

I would say expand, not simplify

binomial coefs, use Pascal's triangle (google it if necessary)
for n = 10
1 10 45 120 210 252 then down again
so

x^10 + 10 x^9 y + 45 x^8 y^2 etc


for n = 5
1 5 10 10 5 1
so
(2a)^5 + 5(2a)^4 (5) + 10(2a)^3(5)^2 ...etc
or
32 a^5 + 400 a^4 + 2000 a^3 etc

Answer 2

why thank you!