EVALUATE :
30 cubed plus space space 20 to the power of 3 space end exponent minus 50 to the power of 3 space space end exponent space W I T H O U T space A C T U A L L Y space C A L C U L A T I N G space T H E space C U B E S space W R I T E space T H E space I D E N T I T Y space U S E D

Asked by Sunny | 24th May, 2017, 07:19: PM

Expert Answer:

Cubic Identity:
 
begin mathsize 14px style 30 cubed plus 20 cubed minus 50 cubed
equals 30 cubed plus 20 cubed plus open parentheses negative 50 cubed close parentheses
Let space straight a equals 30 comma space straight b equals 20 space and space straight c equals negative 50
Now comma space straight a plus straight b plus straight c equals 30 plus 20 minus 50 equals 0
bold Now bold comma bold space bold if bold space bold a bold plus bold b bold plus bold c bold equals bold 0 bold comma bold space bold then bold space bold a to the power of bold 3 bold plus bold b to the power of bold 3 bold plus bold c to the power of bold 3 bold equals bold 3 bold abc
Hence comma
30 cubed plus 20 cubed minus 50 cubed
equals 30 cubed plus 20 cubed plus open parentheses negative 50 cubed close parentheses
equals 3 cross times 30 cross times 20 cross times left parenthesis negative 50 right parenthesis
equals negative 90000 end style

Answered by Rashmi Khot | 25th May, 2017, 08:50: AM