To Know Whether Everyone Knows Identities -1 !
True or False?
x 3 − y 3 = ( x − y ) ( x 2 − x y + y 2 )
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5 solutions
i have seen this proof first time......you are great.....
This problem was asked in my school and many of them did it wrong, So I decided it to post it here !
Good solution
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Thanks for your compliment :)
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Good solutions are always upvoted
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@Rama Devi – Yeah , they must be upvoted. But the upvote must not be taken back after few minutes.
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@Nihar Mahajan – What......................................................
Good but let me know which principle is used?
Gr8 proof!!!!!!!!!!!! never saw that before!!! i agree with @nitish bharadwaj
Thanks bro... awesome solution :)
They are equal if: either x or y equals 0, OR X equals y.
In any other case I can think of, the expressions are not equal
Any ( a 3 ± b 3 ) solves ( a ± b ) ( a 2 ∓ a b + b 2 ) , then x 3 − y 3 = ( x − y ) ( x 2 + x y + y 2 ) , then the answer is "False"
it is poop
Diff of two cubes: (x-y)(x^2+xy+y^2)
Sum of two cubes: (x+y)(x^2-xy+y^2)
Diff of two cubes: (x-y)(x^2+xy+y^2)
A very simple thing to remember: SUM=Positive, Negative, Positive; DIF=Negative, Positive, Positive.
Look at the trinomial - the sign should be the opposite of when the terms of the binomial are multiplied together.
poopybutthead
x 3 − y 3 = x 3 − x 2 y + x 2 y − x y 2 + x y 2 − y 3 = x 2 ( x − y ) + x y ( x − y ) + y 2 ( x − y ) = ( x − y ) ( x 2 + x y + y 2 ) = ( x − y ) ( x 2 − x y + y 2 )