If 20 × 20 = 400, execute the difference of two squares to find 19×21?

I have no idea how to do this. any help would be great please?

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- Mar 25th 2013, 11:24 PMmathkid182help please-hard question
If 20 × 20 = 400, execute the difference of two squares to find 19×21?

I have no idea how to do this. any help would be great please? - Mar 25th 2013, 11:40 PMGusbobRe: help please-hard question
- Mar 26th 2013, 12:03 AMmathkid182Re: help please-hard question
not really im sorry, where did the 20 and the 1 come from? and what would be the next step?

would it be

20^2 - 1^2 = (20-1)(20+1)

400 - 1= 400+20-20-1

399 = 399

?thanks - Mar 26th 2013, 12:12 AMGusbobRe: help please-hard question
- Mar 26th 2013, 12:19 AMmathkid182Re: help please-hard question
Oh i think i get it now thank you so much. do think it would be fine to write the answer as:

=x2 - y2 = (x-y)(x+y)

=20^2 - 1^1 = (20-1)(20+1)

=400-1 = (20-1)(20+1)

=399 = 399

therefore 19x21 = 399

and that would be right? - Mar 26th 2013, 12:30 AMGusbobRe: help please-hard question
I would replace that last line with 399 = 19 x21 instead of 399 = 399. The latter does not actually constitute a proof.

- Mar 26th 2013, 12:32 AMmathkid182Re: help please-hard question
perfect thanks again your a great teacher!!