rbind in a loop with " : " elements

Dear Ruser,
Below, the deal (you can copy paste):

r=3 ; set.seed(1)
v <- matrix(c(rnorm(40)),10,4) 
for (j in 1:4){
    for (i in 1:r){
        x <- t(v[,j]^(i)*v[,1:4]^((r-(4-1)):r))
        print(x)
        }
    }

How to reach to " x " " row bind " inside or outside (preferred) of the
loop. 
To obtain at the end something like:

x

matrix( , 12*4, 10)

Any help or advice is very welcome
Many regards
Bilel



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