Here's a simple one that can be useful.
Suppose you want to multiply 97 x 103 in your head. These are both 3 away from 100, so we can write this as (100–3)(100+3).
Remembering the identity that:
(a-b)(a+b) = a^2-b^2, we get the above product is {100}^2–3^2=10,000-9=9991.
Try 46 x 54. You'll get (50-4)(50+4) which is 2500-16=2484.
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