I'll give one strategy, it is on multiplying not so much big numbers but a little bit.
When multiplying two digit numbers, with a sum of 10 in their ones digit and with the same tens digit.
Ex. 74 x 76 ( they have the same tens digit which is 7 and their ones digit, when add up, it has a total of 10 )
To multiply it easily, just multiply the ones digit ( 4 x 6 = 24 , 24 would be the last two numbers )
then to complete it, just get the number next to the tens digit then multiply to the given original no. ( ex. the tens digit of both numbers is 7, so what's next to 7 is 8 , then multiply both number , 8 x 7 the answer is 56. So, to complete 5624
More examples:⇒
83 x 87 = 7221 ( 8 x 9 = 72 then 3 x 7 = 21 )
48 x 42 = 2016 ( 4 x 5 = 20 then 8 x 2 = 16 )
68 x 62 = 4216 ( 6 x 7 = 42 then 8 x 2 = 16 )
*Remember this will be applicable to the exceptions given or to the explanation above.