If x= 2y+6 then find the value of x3-8y3-36xy-216

Asked by Vanishree | 17th Sep, 2014, 11:06: AM

Expert Answer:

x cubed minus 8 y cubed minus 216 minus 36 x y equals x cubed plus left parenthesis minus 2 y right parenthesis cubed plus left parenthesis minus 6 right parenthesis cubed minus 3 left parenthesis x right parenthesis left parenthesis minus 2 y right parenthesis left parenthesis minus 6 right parenthesis W e space k n o w space t h a t space x cubed plus y cubed plus z cubed minus 3 x y z equals left parenthesis x plus y plus z right parenthesis left parenthesis x squared plus y squared plus z squared minus x y minus y z minus x z right parenthesis equals left parenthesis x minus 2 y minus 6 right parenthesis open curly brackets left parenthesis x right parenthesis squared plus left parenthesis minus 2 y right parenthesis squared plus left parenthesis minus 6 right parenthesis squared minus x left parenthesis minus 2 y right parenthesis minus left parenthesis minus 2 y right parenthesis left parenthesis minus 6 right parenthesis minus x left parenthesis minus 6 right parenthesis close curly brackets equals left parenthesis 2 y plus 6 minus 2 y minus 6 right parenthesis open curly brackets left parenthesis x right parenthesis squared plus left parenthesis minus 2 y right parenthesis squared plus left parenthesis minus 6 right parenthesis squared minus x left parenthesis minus 2 y right parenthesis minus left parenthesis minus 2 y right parenthesis left parenthesis minus 6 right parenthesis minus x left parenthesis minus 6 right parenthesis close curly brackets space space space space space space left square bracket because x equals 2 y plus 6 right square bracket equals 0

Answered by Prasenjit Paul | 17th Sep, 2014, 11:36: AM