43 × 47
The trick, step by step
Check: both start with 4, and 3 + 7 = 10.
Multiply the start by the next number up: 4 × 5 = 20.
Multiply the last digits: 3 × 7 = 21 (always write two digits: 1 × 9 = 09).
Put them side by side: 43 × 47 = 2021.
given working answer taken away
Why it works
(10t + u)(10t + v) = 100t² + 10t(u + v) + uv. When u + v = 10 the middle part is 100t, so the whole is 100t(t + 1) + uv: t(t + 1) hundreds, and uv in the last two digits.
Practise this trick