Question

the volume of a cube is given by 8x3-36x2+54x-27; find the possible expression for the sides of the cube.

Answer 1

Volume of cube= 8x³-36x²+54x-27
l³=8x³-36x²+54x-27
l³=(2x)³-[3.(2x)².3]+3.2x.(3)²-3³
l³=(2x-3)³                                    [∵it is in the form of (a-b)³]
∴l=2x-3
∴suitable expression for edge of cube is 2x-3

Answer 2

The possible side of the cube, a = 2x - 3

Step-by-step explanation:

Given,

The volume of a cube $=8x^3-36x^2+54x-27$

To find, the possible side of the cube = ?

Let the side of the cube = a

We know that,

The volume of the cube $=a^{3}$

∴ $a^{3} =8x^3-36x^2+54x-27$

$a^{3} =(2x)^3-3(2x)^2(3)+3(2x)(3^2)-(3)^3$

Using the algebraic identity,

$(a-b)^{3}=a^{2}-3a^{2}b+3ab^{2}-b^{3}$

Here, a = 2x and b = 3

$a^{3} =(2x-3)^3$

⇒ a = 2x -3

Hence, the possible side of the cube, a = 2x - 3