Archive
24th of March 2017
Mathematics
Q:

Simplify and factorise (a+b+c)2 - (a-b-c)2 + 4b2 - 4c2

Vikas Mahajan - CBSE - Class IX

Friday, March 24, 2017 at 17:09:PM

A:

begin mathsize 16px style left parenthesis straight a plus straight b plus straight c right parenthesis squared space minus space left parenthesis straight a minus straight b minus straight c right parenthesis squared space plus space 4 straight b squared space space minus space 4 straight c squared space
equals straight a squared plus straight b squared plus straight c squared plus 2 ab plus 2 bc plus 2 ac minus left square bracket straight a squared plus straight b squared plus straight c squared minus 2 ab plus 2 bc minus 2 ac right square bracket plus space 4 straight b squared minus 4 straight c squared space
equals straight a squared plus straight b squared plus straight c squared plus 2 ab plus 2 bc plus 2 ac minus straight a squared minus straight b squared minus straight c squared plus 2 ab minus 2 bc plus 2 ac plus space 4 straight b squared minus 4 straight c squared space
equals 2 ab plus 2 bc plus 2 ac plus 2 ab minus 2 bc plus 2 ac plus space 4 straight b squared space minus 4 straight c squared space
equals 4 ab plus 4 ac plus space 4 straight b squared space minus 4 straight c squared space
equals 4 left parenthesis straight b space minus straight c right parenthesis left parenthesis straight b plus straight c right parenthesis plus 4 straight a left parenthesis straight b plus straight c right parenthesis
equals 4 left parenthesis straight b plus straight c right parenthesis left parenthesis straight b minus straight c minus straight a right parenthesis end stylebegin mathsize 16px style left parenthesis straight a plus straight b plus straight c right parenthesis squared space minus space left parenthesis straight a minus straight b minus straight c right parenthesis squared space plus space 4 straight b squared space space minus space 4 straight c squared space
equals straight a squared plus straight b squared plus straight c squared plus 2 ab plus 2 bc plus 2 ac minus left square bracket straight a squared plus straight b squared plus straight c squared minus 2 ab plus 2 bc minus 2 ac right square bracket plus space 4 straight b squared minus 4 straight c squared space
equals straight a squared plus straight b squared plus straight c squared plus 2 ab plus 2 bc plus 2 ac minus straight a squared minus straight b squared minus straight c squared plus 2 ab minus 2 bc plus 2 ac plus space 4 straight b squared minus 4 straight c squared space
equals 2 ab plus 2 bc plus 2 ac plus 2 ab minus 2 bc plus 2 ac plus space 4 straight b squared space minus 4 straight c squared space
equals 4 ab plus 4 ac plus space 4 straight b squared space minus 4 straight c squared space
equals 4 left parenthesis straight b space minus straight c right parenthesis left parenthesis straight b plus straight c right parenthesis plus 4 straight a left parenthesis straight b plus straight c right parenthesis
equals 4 left parenthesis straight b plus straight c right parenthesis left parenthesis straight b minus straight c minus straight a right parenthesis end style

Friday, March 24, 2017 at 17:17:PM