open parentheses 42 close parentheses to the power of 3 space end exponent space minus space open parentheses 18 close parentheses cubed space minus open parentheses 24 close parentheses cubed space e v a l u a t e space i t space w i t h space b y space d o i n g space a c t u a l l y space c a l c u l a t i n g space c u b e s

Asked by KALAPANA.KOTAK | 19th Sep, 2014, 07:10: PM

Expert Answer:

W e space k n o w space t h a t x cubed plus y cubed plus z cubed minus 3 x y z equals open parentheses x plus y plus z close parentheses open parentheses x squared plus y squared plus z squared minus x y minus y z minus z x close parentheses... left parenthesis 1 right parenthesis W e space n e e d space t o space e v a l u a t e comma space open parentheses 42 close parentheses cubed minus open parentheses 18 close parentheses cubed minus open parentheses 24 close parentheses cubed L e t space u s space r e w r i t e space t h e space e x p r e s s i o n space a s comma open parentheses 42 close parentheses cubed minus open parentheses 18 close parentheses cubed minus open parentheses 24 close parentheses cubed equals open parentheses 42 close parentheses cubed plus open parentheses minus 18 close parentheses cubed plus open parentheses minus 24 close parentheses cubed space A p p l y i n g space t h e space i d e n t i t y space left parenthesis 1 right parenthesis comma space w e space h a v e comma space open parentheses 42 close parentheses cubed plus open parentheses minus 18 close parentheses cubed plus open parentheses minus 24 close parentheses cubed space equals open parentheses 42 plus open parentheses minus 18 close parentheses plus open parentheses minus 24 close parentheses close parentheses open square brackets open parentheses 42 close parentheses squared plus open parentheses minus 18 close parentheses squared plus open parentheses minus 24 close parentheses squared minus open parentheses 42 close parentheses open parentheses minus 18 close parentheses minus open parentheses minus 18 close parentheses open parentheses minus 24 close parentheses minus open parentheses minus 24 close parentheses open parentheses 42 close parentheses close square brackets S i n c e space 42 minus 18 minus 24 equals 0 comma space t h e space a b o v e space e q u a t i o n space b e c o m e s space z e r o comma space a n d space h e n c e comma space w e space h a v e space open parentheses 42 close parentheses cubed plus open parentheses minus 18 close parentheses cubed plus open parentheses minus 24 close parentheses cubed space equals 0

Answered by Vimala Ramamurthy | 20th Sep, 2014, 09:14: AM