Binomial Expansions No calculator

Question

‘Show how the binomial expansion can be used to work out $268^2 - 232^2$ without a calculator.’

Also to work out 469 * 548 + 469 * 17 without a calculator.

I understand the process of binomial expansion once you’re given something to expand i.e. $(x+y)^n$, but I don’t understand how to do this without having it written in the form $(x+y)$.

Answer 1

I think you will Need $$268^2-232^2=(268-232)(268+232)$$

Answer 2

$268=232+36$

$268^2=(232+36)^2=232^2+2*232*36+36^2$ which brings in the binomial theorem

$268^2-232^2=2*232*36+36^2=36*(464+36)=36*500=18000$. No calculator required.

but I agree (268+232)*(268-232) is easier