Write the Value of 25³ − 75³ + 50³
Question:
Write the value of \(25^3 – 75^3 + 50^3\).
Solution
We know that
\[ a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca) \]
Let
\[ a=25,\quad b=-75,\quad c=50 \]
Then,
\[ a+b+c=25-75+50 \]
\[ a+b+c=0 \]
Therefore,
\[ a^3+b^3+c^3=3abc \]
Substituting the values:
\[ =3(25)(-75)(50) \]
\[ =-281250 \]
Therefore,
\[ \boxed{-281250} \]