Astrophysics
  • Astrophysics
Difference of squares help
Mathematics
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

Astrophysics
  • Astrophysics
Hey, so I've been wondering about this for a while...we know that \[a^2-b^2 = (a+b)(a-b)\] but that's through distributing, so I have a question, say we never knew the existence of \[(a+b)(a-b)\] how exactly would we prove/ derive \[a^2-b^2 = (a+b)(a-b)\] 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 \[a^2-b^2\] and I don't see exactly how we can derive it mathematically/ or what exactly it would mean without the whole \[(a+b)(a-b)\] Thanks :)
Astrophysics
  • Astrophysics
@Empty Show me your squareception method! @ganeshie8
ganeshie8
  • ganeshie8
More generally : \[x^n-y^n = (x-y)(x^{n-1}+x^{n-2}y+\cdots+xy^{n-2}+y^{n-1})\] but this might be a sledgehammer for the original problem

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

Empty
  • Empty
Well specifically for this one haha: |dw:1436933157294:dw| So the place we want is those two rectangles and the little square there: \[2b(a-b) +(a-b)^2\] factor out an (a-b) term: \[(2b+a-b)(a-b)\] :)
ganeshie8
  • ganeshie8
you don't want to use distributive law is it
Astrophysics
  • Astrophysics
Yeah 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
  • Astrophysics
Actually it can be complicated as well, I just want to see what importance it holds :P
jtvatsim
  • jtvatsim
Here's another geometric derivation: |dw:1436933365159:dw|