QUESTION)prove that (a+b+c)3 –a3-b3-c3= 3(a+b)(b+c)(c+a)

Asked by vrishti TOKAS | 21st May, 2015, 01:23: PM

Expert Answer:

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  L H S left parenthesis a plus b plus c right parenthesis cubed minus a cubed minus b cubed minus c cubed equals left parenthesis a plus b right parenthesis cubed plus c cubed plus 3 left parenthesis a plus b right parenthesis c left parenthesis a plus b plus c right parenthesis minus a cubed minus b cubed minus c cubed space left square bracket U sin g space left parenthesis a plus b right parenthesis cubed equals a cubed plus b cubed plus 3 a b left parenthesis a plus b right parenthesis right square bracket equals a cubed plus b cubed plus 3 a b left parenthesis a plus b right parenthesis plus c cubed plus 3 left parenthesis a plus b right parenthesis c left parenthesis a plus b plus c right parenthesis minus a cubed minus b cubed minus c cubed space equals 3 a b left parenthesis a plus b right parenthesis plus 3 left parenthesis a plus b right parenthesis c left parenthesis a plus b plus c right parenthesis equals 3 left parenthesis a plus b right parenthesis left square bracket a b plus c a plus c b plus c squared right square bracket equals 3 left parenthesis a plus b right parenthesis left square bracket a left parenthesis b plus c right parenthesis plus c left parenthesis b plus c right parenthesis right square bracket equals 3 left parenthesis a plus b right parenthesis left parenthesis b plus c right parenthesis left parenthesis c plus a right parenthesis equals R H S H e n c e space P r o v e d. space Y o u space c a n space a l s o space r e m e m b e r space t h i s space a s space a space f o r m u l a e. space U s e f u l space i n space f a c t o r i z i n g space A l g e b r a i c space E x p r e s s i o n s.

Answered by Prasenjit Paul | 22nd May, 2015, 09:41: AM

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