Question

(a-b)^3+(b-c)^3+(c-a)^3=?

plz gimme an answer fast plz

Answer 1

Answer:

3 ( a - b ) ( b - c ) ( c - a )

Step-by-step explanation:

To find --->

( a - b )³ + ( b - c )³ + ( c - a )³ = ?

Solution---> We have an identity

If a + b + c = 0 , then

a³+ b³ + c³ = 3abc

Let , ( a - b ) = p , ( b - c ) = q , ( c - a ) = r

p + q + r = ( a - b ) + ( b - c ) + ( c - a )

= a - a + b - b + c - c

p + q + r = 0

So , p³ + q³ + r³ = 3pqr

( a - b )³+( b - c )³+ (c - a )³ =3 (a - b ) ( b - c ) ( c - a )

Similar question--->

(1) ( a² - b² )³ + ( b² - c² )³ + ( c² - a² )³

(2) a³ ( b - c )³ + b³ ( c - a )³ + c³ ( a - b )³

(3) a⁶ ( b² - c² )³ + b⁶ ( a² - c² ) + c⁶ (a² - b² )

Other identities --->

(1) a² - b² = ( a + b ) ( a - b )

(2) (a + b )² = a² + b² + 2ab

(3) ( a - b )² = a² + b² - 2ab

(4) (a + b + c )² = a² + b² + c² + 2ab + 2bc + 2ca

(5) (a + b )³ = a³ + b³ + 3ab ( a + b )

(6) (a - b )³ = a³ - b³ - 3ab ( a - b )