2( 7 )³ + 2( 9)³ + 2( 13 )³ - 6 × 7 × 9 ×13
Suppose ,
7 = x , 9 = y and 13 = z
Now,
= 2x³ + 2y³ + 2z³ - 6xyz
Using identity :
= 2x³ +2y³ +2z³- 6xyz= (x+y+z) [(x-y)² +(y-z)² +(z-x)² ]
By putting the value of x,y and z.
= ( 7+9+13 ) { ( 7-9 )² + ( 9-13)² + ( 13-7 )² }
= ( 29 ) { ( -2 )² + ( -4 )² + ( 6 )² }
= 29 ( 4 + 16 + 36 )
= 29 × 56
= 1624