Question

Hi i am confused in a problem :

a^2-b^2=(a+b)(a-b)
right?

now i have to prove that
a^2-b^2=(a+b)(a-b)

I know that RHS can be expanded and this formula can be proved but m confused how to do that by just taking LHS ??

Help please

Answer 1

I hope that you all got what I meant to say..

Answer 2

\[a^2-b^2+ab-ab=a^2+ab-b^2-ab=a(a+b)-b(a+b)\]does that help?

Answer 3

add ab and subtract ab.......... and factor it

Answer 4

oh i got it thanks a lot @mukushla and @sauravshakya

thanks again.. that was just a small confusion that is resolved now.. thanks

Answer 5

Welcome...

Answer 6

yw :)

Answer 7

What the...@mathslover, I assumed you already knew this kinda stuff.

Answer 8

Nice time-passing methods.

Answer 9

@Hero i knew that stuff but not about that LHS ..

sometimes "genius" persons also make mistake..
but I am not so genius.

It was not time pass @saifoo.khan

Answer 10

since we can expand the RHS, why would we need to reprove it using the LHS?

Answer 11

It was my curiousness ...

Answer 12

for example we have proof for
(a+b)^2=a^2+b^2+2ab

we can proove that by using LHS also

Answer 13

\[{(a+b)^2=(a+b)(a+b)=a(a+b)+b(a+b)\\=a^2+ab+ba+b^2=a^2+2ab+b^2}\]

Answer 14

(a+b)(a+b)

Answer 15

right

Answer 16

im not sure if i would call these proofs, moreso the results of using appropriate mathings

Answer 17

good point "sir"

Answer 18

if you can work out one side to get to the other; the proof of the other side is just the reversing of the steps

Answer 19

Yep

Answer 20

a^2 - b^2 = a^2 + b^2 - 2b^2 + 2ab - 2ab = (a+b)^2 - 2b(a+b) =>(a+b)(a-b)

there must be many more methods !