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A cube with side length 4p is stacked on another cube with side length 2q^2. What is the total volum...
5 months ago
Q:
A cube with side length 4p is stacked on another cube with side length 2q^2. What is the total volume of the cubes in factored form?
Accepted Solution
A:
Volume of the cube with side 4p = 4p x 4p x 4p = 64p³
Volume of the cube with side 2q² = 2q² x 2q² x 2q² = 8q⁶
Total Volume = 64p³ + 8q⁶
Total Volume = (4p)³ + (2q²)³
Total Volume = (4p + 2q²)( ( 4p)² - (4p)(2q²) + (2q²)²)
Total Volume = (4p + 2q²)( 16p² - 8pq² + 4q⁴)
Answer: (4p + 2q²)( 16p² - 8pq² + 4q⁴)