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Astrophysics
 one year ago
Difference of squares help
Astrophysics
 one year ago
Difference of squares help

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Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0Hey, so I've been wondering about this for a while...we know that \[a^2b^2 = (a+b)(ab)\] but that's through distributing, so I have a question, say we never knew the existence of \[(a+b)(ab)\] how exactly would we prove/ derive \[a^2b^2 = (a+b)(ab)\] I know there maybe geometry but is there a way using algebra, other methods, actually anything will be useful, as I don't find anything intuitive about \[a^2b^2\] and I don't see exactly how we can derive it mathematically/ or what exactly it would mean without the whole \[(a+b)(ab)\] Thanks :)

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0@Empty Show me your squareception method! @ganeshie8

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2More generally : \[x^ny^n = (xy)(x^{n1}+x^{n2}y+\cdots+xy^{n2}+y^{n1})\] but this might be a sledgehammer for the original problem

Empty
 one year ago
Best ResponseYou've already chosen the best response.0Well specifically for this one haha: dw:1436933157294:dw So the place we want is those two rectangles and the little square there: \[2b(ab) +(ab)^2\] factor out an (ab) term: \[(2b+ab)(ab)\] :)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2you don't want to use distributive law is it

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0Yeah pretty much, that's nice empty haha. I just want to see if there are other methods that even a 5 year old could understand

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0Actually it can be complicated as well, I just want to see what importance it holds :P

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3Here's another geometric derivation: dw:1436933365159:dw