MATH SOLVE

8 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)

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)