To Know whether all know identities

Algebra Level 2

True or False ?

( x − y ) 3 = x 3 − y 3 + 3 x y ( x − y . ) (x-y)^3=x^3-y^3+3xy(x-y.)

Cannot determine False True

Rama Devi by Rama Devi , 43, India

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4 solutions

Replace x 3 − y 3 = ( x − y ) 3 + 3 x y ( x − y ) x^{3}-y^{3} = (x-y)^{3}+3xy(x-y)

⇒ ( x − y ) 3 = [ ( x − y ) 3 + 3 x y ( x − y ) ] + 3 x y ( x − y ) = ( x − y ) 3 + 6 x y ( x − y ) \Rightarrow (x-y)^{3}=[(x-y)^{3}+ 3xy(x-y)] +3xy(x-y) =(x-y)^{3}+ 6xy(x-y)

Therefore, ( x − y ) 3 ≠ x 3 − y 3 + 3 a b ( a − b ) (x-y)^{3} \not= x^{3}-y^{3}+3ab(a-b) , which is F a l s e \boxed{False}

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Vishwash Kumar
Nov 2, 2016

Yeah , It can be true in case that x becomes equal to y . You should have provided it x is not equal to y

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Arulx Z
Aug 17, 2015

It must be

x 3 − y 3 − 3 x y ( x − y ) { x }^{ 3 }-{ y }^{ 3 }-3xy(x-y)

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Azadali Jivani
Aug 14, 2015

(x-Y)^3 = X^3 - Y^3 - 3X^2 + XY^2 (Ans.)

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Once check your solution properly.

Rama Devi - 5 years, 10 months ago

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Did this question was inspired by my question ? Isn't it .

Anish Harsha - 5 years, 10 months ago

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