We are required to find the difference in the volume of the cubes
The difference in the volume of the cubes is 4(4x⁴ - 9y²)
side length of small cube = 6y
volume of small cube = (side length)²
= (6y)²
side length of larger cube = 4x²
volume of larger cube = (side length)²
= (4x²)²
Difference in volume = volume of larger cube - volume of small cube
= (4x²)² - (6y)²
= (4x²)(4x²) - 36y²
= 16x⁴ - 36y²
= 4(4x⁴ - 9y²)
Therefore, the difference in the volume of the cubes is 4(4x⁴ - 9y²)
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