Question

(a − b)³ + (b − c)³ + (c − a)³ =

पर्याय

• (a + b + c) (a² + b² + c² − ab − bc − ca)

• (a − b) (b − c) (c − a)

• 3(a − b) ( b− c) (c − a)

• none of these

Answer 1

Given   ${\displaystyle {(a-b)}^3+{(b-c)}^3+{(c-a)}^2}$

Using identity    ${\displaystyle x^2+y^3+z^3=3xyz}$

Here  ${\displaystyle x=a-b,y=b-c,z=c-a}$

${\displaystyle {(a-b)}^3+{(b-c)}^3{(c-a)}^3=3(a-b)(b-c)(c-a)}$

Hence the Value of  ${\displaystyle {(a-b)}^3+{(b-c)}^3+{(c-a)}^3}$ is  ${\displaystyle 3(a-b)(b-c)(c-a)}$