Without actually calculating the cubes, find the value of each of the following:

${\left(-12\right)}^3+{\left(7\right)}^3+{\left(5\right)}^3$

Without actually calculating the cubes, find the value of each of the following:

${\left(28\right)}^3+{\left(-15\right)}^3+{\left(-13\right)}^3$

Give possible expressions for the length and breadth of the rectangle whose area is $25a^2-35a+12$.

Give possible expressions for the length and breadth of the rectangle whose area is $35y^2+13y-12$.

What are the possible expressions for the dimensions of the cuboid whose volume is $3x^2-12x$.

What are the possible expressions for the dimensions of the cuboid whose volume is $12k{y}^2+8ky-20k$.

What is the possible expression for the dimensions of the cuboids whose volumes are given below?

Volume: $12k{y}^2+8ky-20k$