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I've got an app on my phone that DS enjoys called 'Epic Maths Tricks'. I can't comment on it myself because he's better at maths than me so I don't get what he's doing half of the time and have to check his answers with a calculator
DS (who is 10) was moaning in the toy shop earlier because we were looking at toys for his sister, and so to keep him quiet I asked him 26x26, 28x28, etc., which didn't take him long, so gave him 112x112, which he said was 14 squared times 8 squared (which is true), and came up with the answer I think based on 14^2  x 8 x 2 x 2 x 2.
Anyway are there any tricks to do harder mental arithmetic that I could perhaps teach him?