# Binomial Expansions No calculator

‘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 $(x+y)$.

• $a^2 - b^2 = (a+b)(a-b)$. Not sure how binomial expansion enters, maybe it's a typo? – angryavian May 15 '18 at 18:57
• I think the question refers to $x^2-y^2=(x+y)(x-y)$ – G Cab May 15 '18 at 18:59
• or $268^2-232^2=(232+36)^2-232^2= 2\cdot36\cdot232+36^6$ – G Cab May 15 '18 at 19:04

$268=232+36$
$268^2=(232+36)^2=232^2+2*232*36+36^2$ which brings in the binomial theorem
$268^2-232^2=2*232*36+36^2=36*(464+36)=36*500=18000$. No calculator required.
$268^2-232^2=(268+232)(268-232)$...
I think you will Need $$268^2-232^2=(268-232)(268+232)$$