Question

Without actual multiplication find the value of (17)3(_12)3(_5)3

Answer 1

Using the formula,
${x}^{3} + {y}^{3} + {z}^{3} - 3xyz = ( {x}^{2} + {y}^{2} + {z}^{2} - xy - yz - zx)(x + y + z)$
Here we find that
x=17
y=-12
z=-5
x+y+z=0
So, the above problem will be given by
3xyz
=3×17×-5×-12
=1020.