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‘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 $(x+y)$.

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    $\begingroup$ $a^2 - b^2 = (a+b)(a-b)$. Not sure how binomial expansion enters, maybe it's a typo? $\endgroup$
    – angryavian
    Commented May 15, 2018 at 18:57
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    $\begingroup$ I think the question refers to $x^2-y^2=(x+y)(x-y)$ $\endgroup$
    – G Cab
    Commented May 15, 2018 at 18:59
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    $\begingroup$ or $268^2-232^2=(232+36)^2-232^2= 2\cdot36\cdot232+36^6$ $\endgroup$
    – G Cab
    Commented May 15, 2018 at 19:04

2 Answers 2

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$268=232+36$

$268^2=(232+36)^2=232^2+2*232*36+36^2$ 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

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

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