Question

Without actually calculating the cubes find the 45³-25³-20³

Answer 1

a=45
b= -25
c= -20
 if a+b+c=0 then a³+b³+c³=3abc
45+(-25)+(-20)
45-25-20=0
 so 45³-25³-20³ =3×45×-25×-20
                         =67500
                         

Answer 2

If a+b+c=0 then, we say that a^3+b^3+c^3=3abc
Here, 45+(-25)+(-20)= 45-25-20= 45-45=0
So, a cube+ b cube+ c cube= 3abc
=3(45)(-25)(-20)
=3*45*25*20 (two minus will cancel each other in multiplication)
By multiplying we will get, 67500.
So finally, this is your answer.