Write the Value of 48³ − 30³ − 18³
Question:
Write the value of \(48^3 – 30^3 – 18^3\).
Solution
Let
\[ a=48,\quad b=-30,\quad c=-18 \]
Then,
\[ a+b+c=48-30-18 \]
\[ a+b+c=0 \]
We know that if \(a+b+c=0\), then
\[ a^3+b^3+c^3=3abc \]
Therefore,
\[ 48^3-30^3-18^3 =3(48)(-30)(-18) \]
\[ =77760 \]
Therefore,
\[ \boxed{77760} \]