Question

Without actually calculating the cubes, find the value of ${45}^3-{25}^3-{20}^3$

Answer 1

Let $a=45,b=-25,c=-20$

$a+b+c=0$

Therefore,

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

$(45{)}^3+(-25{)}^3+(-20{)}^3=3\times 45\times (-25)\times (-20)=67500$

(45)3+(−25)3+(−20)3=3×45×(−25)×(−20)=67500