Help In Factor Theorem Question?

Question

The edge length of a cube is 2x-1 units. The volume of a larger cube is 8x^2 +12x^2 +6x+1 how do the edge lengths of the two cubes compare?

Answer 1

Given that volume of the larger cube as .

Side of a smaller cube is 2x - 1.

We can clearly see that volume is can be written as 

Therefore the side of the larger cube is 2x + 1.

Now take x = 1 then

side of smaller cube = 1

side of the larger cube = 2

Now take x = 2 then

side of smaller cube = 3

side of the larger cube = 5

Now if we compare the sides of the smaller and larger cube then we can observe that the larger cube is 2 units more than the smaller cube.