What is the volume of a cube with a side length of 4x² + 3?

The volume of a cube is calculated using the formula: Volume = s³, where s represents the length of a side of the cube.

In this case, the side length s is given as 4x² + 3. To find the volume, we need to substitute this expression into the volume formula:

Volume = (4x² + 3)³

Next, we can expand this expression:

• First, let’s calculate (4x² + 3)²:
• (4x² + 3)(4x² + 3) = 16x^4 + 24x² + 9

Now, we multiply this result by (4x² + 3) once more:

• Volume = (4x² + 3)(16x^4 + 24x² + 9)
• = 64x^6 + 96x^4 + 36x² + 48x^4 + 72x² + 27
• = 64x^6 + (96x^4 + 48x^4) + (36x² + 72x²) + 27
• = 64x^6 + 144x^4 + 108x² + 27

Hence, the volume of the cube is:

Volume = 64x⁶ + 144x⁴ + 108x² + 27

In summary, the expression for the volume of a cube with side length 4x² + 3 is:

V = 64x⁶ + 144x⁴ + 108x² + 27.