The partial product method involves multiplying each digit of a number in turn with each digit of another where each digit maintains its place. (So, the 2 in 23 would actually be 20.) For instance, 23 x 42 would become (20 x 40) + (20 x 2) + (3 x 40) + (3 x 2).
Therefore for your question you would do:
- 40x 10
+ 40 x 7
+ 10 x 3
+ 3 x 7
= 400 + 280 + 30 + 22
= 732
