a cubed space plus space b to the power of 2 space space end exponent plus space c to the power of 3 space end exponent space minus space 3 a b c space equals space left parenthesis a plus b plus c right parenthesis left parenthesis a to the power of 2 space end exponent plus space b to the power of 2 space end exponent space plus space c to the power of 2 space end exponent space minus a b space minus b c minus space c a right parenthesis
prove it without using squars or geometry just by algebra. Simplify a to the power of 3 space end exponent plus space b to the power of 3 space end exponent space plus space c cubed space minus 3 a b c
 

Asked by agrawalritik369 | 10th Jul, 2014, 03:19: PM

Expert Answer:

L e t space u s space e x p a n d space left parenthesis a plus b plus c right parenthesis cubed : space left parenthesis a plus b plus c right parenthesis cubed equals a cubed plus open parentheses b plus c close parentheses cubed plus 3 a open parentheses b plus c close parentheses squared plus 3 a squared open parentheses b plus c close parentheses equals a cubed plus b cubed plus c cubed plus 3 b squared c plus 3 b c squared plus 3 a open parentheses b squared plus c squared plus 2 b c close parentheses plus 3 a squared b plus 3 a squared c equals a cubed plus b cubed plus c cubed plus 3 b squared c plus 3 b c squared plus 3 a b squared plus 3 a c squared plus 6 a b c plus 3 a squared b plus 3 a squared c plus 6 a b c equals a cubed plus b cubed plus c cubed plus 3 a b open square brackets a plus b close square brackets plus 3 b c open square brackets b plus c close square brackets plus 3 a c open square brackets a plus c close square brackets plus 6 a b c rightwards double arrow a cubed plus b cubed plus c cubed space minus 3 a b c equals left parenthesis a plus b plus c right parenthesis cubed minus 3 a b open square brackets a plus b close square brackets minus 3 b c open square brackets b plus c close square brackets minus 3 a c open square brackets a plus c close square brackets minus 9 a b c rightwards double arrow a cubed plus b cubed plus c cubed space minus 3 a b c equals left parenthesis a plus b plus c right parenthesis cubed minus 3 a b open square brackets a plus b plus c close square brackets minus 3 b c open square brackets b plus c plus a close square brackets minus 3 a c open square brackets a plus c plus b close square brackets rightwards double arrow a cubed plus b cubed plus c cubed space minus 3 a b c equals open square brackets a plus b plus c close square brackets open square brackets left parenthesis a plus b plus c right parenthesis squared minus 3 a b minus 3 b c minus 3 a c close square brackets rightwards double arrow a cubed plus b cubed plus c cubed space minus 3 a b c equals open square brackets a plus b plus c close square brackets open square brackets a squared plus b squared plus c squared plus 2 a b plus 2 b c plus 2 c a minus 3 a b minus 3 b c minus 3 a c close square brackets rightwards double arrow a cubed plus b cubed plus c cubed space minus 3 a b c equals open square brackets a plus b plus c close square brackets open square brackets a squared plus b squared plus c squared minus a b minus b c minus a c close square brackets

Answered by Vimala Ramamurthy | 11th Jul, 2014, 11:26: AM

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