Evaluate:
\[ 48^3 – 30^3 – 18^3 \]
Solution:
Rewrite the expression:
\[ 48^3 + (-30)^3 + (-18)^3 \]
Since, \[ 48-30-18=0 \]
Using identity:
\[ a^3+b^3+c^3=3abc \quad \text{when} \quad a+b+c=0 \]
Take \[ a=48,\qquad b=-30,\qquad c=-18 \]
\[ 48+(-30)+(-18)=0 \]
Therefore, \[ 48^3-30^3-18^3 = 3(48)(-30)(-18) \]
\[ = 77760 \]