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ICSE Class 9 Answered

Factorize
 
 
27 (a+2b)^3 +(a+6b)^3
Asked by rgkgmu | 03 Mar, 2016, 07:06: PM
answered-by-expert Expert Answer
begin mathsize 16px style 27 left parenthesis a plus 2 b right parenthesis cubed plus left parenthesis a plus 6 b right parenthesis cubed equals 3 cubed left parenthesis a plus 2 b right parenthesis cubed plus left parenthesis a plus 6 b right parenthesis cubed equals left square bracket 3 left parenthesis a plus 2 b right parenthesis right square bracket cubed plus left parenthesis a plus 6 b right parenthesis cubed U sin g space i d e n t i t y space x cubed plus y cubed equals left parenthesis x plus y right parenthesis left parenthesis x squared minus x y plus y squared right parenthesis comma space w e space h a v e equals left square bracket 3 left parenthesis a plus 2 b right parenthesis plus left parenthesis a plus 6 b right parenthesis right square bracket left curly bracket left square bracket 3 left parenthesis a plus 2 b right parenthesis right square bracket squared minus 3 left parenthesis a plus 2 b right parenthesis left parenthesis a plus 6 b right parenthesis plus left parenthesis a plus 6 b right parenthesis squared right curly bracket equals left square bracket 3 a plus 6 b plus a plus 6 b right square bracket left curly bracket left square bracket 9 left parenthesis a squared plus 4 a b plus 4 b squared right parenthesis minus 3 left parenthesis a squared plus 6 a b plus 2 a b plus 12 b squared right parenthesis plus left parenthesis a squared plus 12 a b plus 36 b squared right parenthesis right curly bracket equals left square bracket 4 a plus 12 b right square bracket left square bracket 9 a squared plus 36 a b plus 36 b squared minus 3 a squared minus 24 a b minus 36 b squared plus a squared plus 12 a b plus 36 b squared right square bracket equals 4 left square bracket a plus 3 b right square bracket left square bracket 9 a squared minus 3 a squared plus a squared plus 36 a b minus 24 a b plus 12 a b plus 36 b squared minus 36 b squared plus 36 b squared right square bracket equals 4 left square bracket a plus 3 b right square bracket left square bracket 7 a squared plus 24 a b plus 36 b squared right square bracket end style
Answered by Rashmi Khot | 04 Mar, 2016, 11:38: AM

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