Question

Evaluate:

25³ − 75³ + 50³

Answer 1

In the given problem we have to evaluate the following

 Given  25³ − 75³ + 50³

We shall use the identity  `a^3 + b^3 +c^3 -3abc = (a+b+c)(a^2 + b^^2 + c^2 - ab - bc - ca)`

Let Take  a = 25,b = 75,c = 50

`a^3 + b^3 + c^3 (a+b+c) (a^2+b^2 + c^2 - ab - bc -ca)`

` a^3 + b^3 + c^3 = (a+b+c)(a^2 + b^2 + c^2 -ab - bc-ca) + 3abc`

`a^3 + b^3+ b^3 = (-75 + 25 -50)(a^2 + b^2 + c^2 - ab =bc - ca) + 3abc`

`a^3 + b^3 + c^3 = 0 xx (a^2 + b^2 c^2 - ab - bc - ca) + 3abc`

`a^3+ b^3+c^3 = +3abc`

`25^3 - 75^3+50^3 = 3 xx 25 xx 50 xx -75`

` = -281250`

Hence the value of 25³ − 75³ + 50³ is` -281250`.