Many students go wow when I evaluate workings, without a GC. I’m not showing off, but it is because I don’t really carry a calculator with me. haha. So some students do ask me how I evaluate the square of numbers so quickly. I thought, in light of A-level’s coming, I should share something interesting.

Firstly, we trace back to a formula that we saw in primary school.

(a+b)^2 = a^x + 2ab + b^2

This formula is really going to be the core of us solving any square of numbers.

Next, we just need to split the number that you want to square effectively. So consider,

63 = 60 +3
63^3 = (60+3)^2 = 60^2 + 2(60)(3) + 3^2

Some students will ask why not use (a-b)^2 instead. This is plausible, but we usually are better with addition than multiplication hah.

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