R spreading multiple columns with tidyr

Take this sample variable

df <- data.frame(month=rep(1:3,2),
                 student=rep(c("Amy", "Bob"), each=3),
                 A=c(9, 7, 6, 8, 6, 9),
                 B=c(6, 7, 8, 5, 6, 7))

I can use spread from tidyr to change this to wide format.

> df[, -4] %>% spread(student, A)
  month Amy Bob
1     1   9   8
2     2   7   6
3     3   6   9

But how can I spread two values e.g. both A and B, such that the output is something like

  month Amy.A Bob.A Amy.B Bob.B
1     1     9     8     6     5
2     2     7     6     7     6
3     3     6     9     8     7

Here's a possible both simple and very efficient solution using data.table

library(data.table) ## v >= 1.9.6
dcast(setDT(df), month ~ student, value.var = c("A", "B")) 
#    month Amy_A Bob_A Amy_B Bob_B
# 1:     1     9     8     6     5
# 2:     2     7     6     7     6
# 3:     3     6     9     8     7

Or a possible tidyr solution

df %>% 
  gather(variable, value, -(month:student)) %>%
  unite(temp, student, variable) %>%
  spread(temp, value)

#   month Amy_A Amy_B Bob_A Bob_B
# 1     1     9     6     8     5
# 2     2     7     7     6     6
# 3     3     6     8     9     7

---

EDIT 22/10/2019

As mentioned in comments by @gjabel, newer tidyr versions (v1.0.0+) have now pivot_wider and pivot_longer functions (currently in maturing state), hence, a newer approach would be

pivot_wider(data = df, 
            id_cols = month, 
            names_from = student, 
            values_from = c("A", "B"))
# # A tibble: 3 x 5
#     month A_Amy A_Bob B_Amy B_Bob
#     <int> <dbl> <dbl> <dbl> <dbl>
#   1     1     9     8     6     5
#   2     2     7     6     7     6
#   3     3     6     9     8     7