Q11

Prove that left parenthesis a plus b plus c right parenthesis cubed minus a cubed minus b cubed minus c cubed equals 3 left parenthesis a plus b right parenthesis left parenthesis b plus c right parenthesis left parenthesis c plus a right parenthesis.

Asked by kishor.kp14 | 18th Jun, 2019, 11:20: AM

Expert Answer:

begin mathsize 16px style straight L. straight H. straight S space equals space left parenthesis straight a space plus space straight b space plus space straight c right parenthesis cubed space minus space straight a cubed space minus space straight b cubed space minus space straight c cubed
space space space space space space space space space space equals space open square brackets open parentheses straight a space plus space straight b close parentheses space plus straight c close square brackets cubed space minus space straight a cubed space minus space straight b cubed space minus space straight c cubed
space space space space space space space space space space equals space left parenthesis straight a space plus space straight b right parenthesis cubed space plus space straight c cubed space plus space 3 straight c left parenthesis straight a space space plus space straight b right parenthesis open parentheses straight a space plus space straight b space plus space straight c close parentheses space minus space straight a cubed space minus space straight b cubed space minus space straight c cubed space space space space space space... space since space left parenthesis straight x space plus space straight y right parenthesis cubed space equals space straight x cubed space plus space straight y cubed space plus space 3 xy left parenthesis straight x space plus space straight y right parenthesis
space space space space space space space space space space equals space space straight a cubed space plus space straight b cubed space plus straight c cubed plus space 3 ab left parenthesis straight a space plus space straight b right parenthesis space plus space 3 straight c left parenthesis straight a space space plus space straight b right parenthesis open parentheses straight a space plus space straight b space plus space straight c close parentheses space minus space straight a cubed space minus space straight b cubed space minus space straight c cubed space space
space space space space space space space space space space equals space 3 ab left parenthesis straight a space plus space straight b right parenthesis space space plus space space 3 straight c left parenthesis straight a space space plus space straight b right parenthesis open parentheses straight a space plus space straight b space plus space straight c close parentheses
space space space space space space space space space space equals 3 left parenthesis straight a space plus space straight b right parenthesis open parentheses ab space plus space ac space plus space bc space plus space straight c squared close parentheses
space space space space space space space space space space equals 3 left parenthesis straight a space plus space straight b right parenthesis open square brackets straight a left parenthesis straight b space plus space straight c right parenthesis space plus space straight c left parenthesis straight b space plus space straight c right parenthesis close square brackets
space space space space space space space space space space equals 3 left parenthesis straight a space plus straight b right parenthesis left parenthesis straight b space plus space straight c right parenthesis left parenthesis straight c space plus space straight a right parenthesis
space space space space space space space space space space equals space straight R. straight H. straight S
Hence space proved. end style

Answered by Yasmeen Khan | 18th Jun, 2019, 12:00: PM