A cube with side length 5h^2 is stacked on another cube with side length 3k What is the total volume of the cubes in factored form?
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The first one :
(5h²)³
The second one:
(3k)³
Add them together:
(5h²)³ + (3k)³
Since you now have the sum of two cubes, you can factor it as:
x³ + y³ = (x + y)(x² - xy + y²)
Substitute 5h² for x and 3k for y to get:
(5h² + 3k)((5h²)² - 5h(3k) + (3k)²)
simplify:
(5h² + 3k)(25h⁴ - 15hk + 9k²)
(answer B)
(5h²)³
The second one:
(3k)³
Add them together:
(5h²)³ + (3k)³
Since you now have the sum of two cubes, you can factor it as:
x³ + y³ = (x + y)(x² - xy + y²)
Substitute 5h² for x and 3k for y to get:
(5h² + 3k)((5h²)² - 5h(3k) + (3k)²)
simplify:
(5h² + 3k)(25h⁴ - 15hk + 9k²)
(answer B)
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