Question

Without actually calculating the cube find the value of the following ; $(2.8{)}^3+(-1.5{)}^3+(-1.3{)}^3$

Answer 1

Let $x=2.8,y=-1.5,z=-1.3$

We know that,

$x^3+y^3+z^3-3xyz=(x+y+z)(x^2+y^2+z^2-xy-xz-yz)$

Here,

$x+y+z=2.8-1.5-1.3=0$

So,

$x^3+y^3+z^3-3xyz=0$

$x^3+y^3+z^3=3xyz$

$(2.8{)}^3+(-1.5{)}^3+(-1.3{)}^3=3(2.8\left)\right(-1.5\left)\right(-1.3)=16.38$