Evaluate:
\[ 25^3 – 75^3 + 50^3 \]
Solution:
Rewrite the expression:
\[ 25^3 + 50^3 – 75^3 \]
Since, \[ 25+50=75 \]
Using identity:
\[ a^3+b^3+c^3=3abc \quad \text{when} \quad a+b+c=0 \]
Take \[ a=25,\qquad b=50,\qquad c=-75 \]
\[ 25+50-75=0 \]
Therefore, \[ 25^3+50^3-75^3 = 3(25)(50)(-75) \]
\[ = -281250 \]