Question:Evaluate following expressions:
 i) `( 527 xx 527 xx 527 + 183 xx 183 xx 183)/(527 xx 527 - 527 xx 183 + 183 xx 183)`
 
 ii) `(458 xx 458 xx 458 - 239 xx 239 xx 239)/(458 xx 458 xx + 458 xx 239 + 239 xx 239)`

 iii) `((614 + 168)^2 - (614 - 168)^2)/(614 xx 168)`

 iv) `((832 + 278)^2 + (832 - 278)^2)/(832 xx 832 + 278 xx 278)` 

Answer i) Given Expression 

 `= ((527)^3 + (183)^3)/((527)^2 - 527 xx 183 + (183)^2)`

 `= (a^3 + b^3)/(a^2 - ab + b^2)`

 `= (a + b) = (527 + 183) + 710)`


 ii) Given Expression 

 `= ((458)^3-(239)^3)/((458)^2 + 458 xx 239 + (239)^2)`

 `= (a^3-b^3)/(a^2 + ab + b^2)`

 `= (a - b) = (457 - 239) = 219)`


 iii) Given Expression

 `= ((a + b)^2 - (a - b)^2)/(ab)` 

 `= (4ab)/4`

 `= 4`


 iv) Given Expression

 `= ((a + b)^2 + (a - b)^2)/(a^2 + b^2)`

 `= (2(a^2 + b^2))/(a^2 + b^2)`

 `= 2` 

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Mohammad Towhidul Islam

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