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CBSE Class 9 Answered

Prove (a+b+c)^3 - a^3 - b^3 - c^3 = 3(a+b) (b+c) (c+a)
Asked by kirtiagarwal148 | 07 Jun, 2018, 07:49: PM
answered-by-expert Expert Answer
begin mathsize 16px style open parentheses straight a plus straight b plus straight c close parentheses cubed space equals space open square brackets straight a space plus space left parenthesis straight b space plus thin space straight c right parenthesis close square brackets cubed equals straight a cubed space plus space 3 straight a open parentheses straight b plus straight c close parentheses open square brackets straight a space plus space left parenthesis straight b space plus thin space straight c right parenthesis close square brackets plus left parenthesis straight b space plus thin space straight c right parenthesis cubed equals straight a cubed space plus space 3 straight a open parentheses straight b plus straight c close parentheses open square brackets straight a space plus space left parenthesis straight b space plus thin space straight c right parenthesis close square brackets space plus space straight b cubed space plus space 3 bc open parentheses straight b plus straight c close parentheses space plus space straight c cubed equals space straight a cubed space plus space straight b cubed space plus space straight c cubed space plus 3 straight a open parentheses straight b plus straight c close parentheses open square brackets straight a space plus space left parenthesis straight b space plus thin space straight c right parenthesis close square brackets space plus space 3 bc open parentheses straight b plus straight c close parentheses equals straight a cubed space plus space straight b cubed space plus space straight c cubed space plus space 3 left parenthesis straight b space plus space straight c right parenthesis open square brackets straight a squared space plus space ab space plus space ac plus space bc close square brackets equals straight a cubed space plus space straight b cubed space plus space straight c cubed space plus space 3 left parenthesis straight b space plus space straight c right parenthesis open square brackets straight a left parenthesis straight a plus straight b right parenthesis thin space plus thin space straight c left parenthesis straight a space plus space straight b right parenthesis close square brackets equals straight a cubed space plus space straight b cubed space plus space straight c cubed space plus space 3 left parenthesis straight b space plus thin space straight c right parenthesis left parenthesis straight a space plus space straight b right parenthesis left parenthesis straight a space plus space straight c right parenthesis open parentheses straight a plus straight b plus straight c close parentheses cubed space minus space straight a cubed space minus space straight b cubed space minus space straight c cubed space equals space 3 left parenthesis straight b space plus thin space straight c right parenthesis left parenthesis straight a space plus space straight b right parenthesis left parenthesis straight a space plus space straight c right parenthesis end style
Answered by Sneha shidid | 08 Jun, 2018, 11:44: AM

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