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A new office building in town has x² + 4 floors. Each floor is 3x² – 5 feet high. Which expression shows the total height of this office building?
3x⁴ – 20 feet
4x² – 1 feet
3x⁴ + 7x² – 20 feet
4x⁴ + 6x² – 20 feet
To find the total height of the office building, we need to multiply the number of floors by the height of each floor.
The number of floors is given by (x^2 + 4), and the height of each floor is (3x^2 – 5).
So, the total height (H) can be calculated as:
[
H = (text{number of floors}) times (text{height of each floor})
]
[
H = (x^2 + 4)(3x^2 – 5)
]
Now let’s expand this expression:
1. Distribute (x^2):
[
x^2 cdot 3x^2 = 3x^4
]
[
x^2 cdot (-5) = -5x^2
]
2. Distribute (4):
[
4 cdot 3x^2 = 12x^2
]
[
4 cdot (-5) = -20
]
3. Combine all the results:
[
H = 3x^4 + (-5x^2 + 12x^2) – 20
]
[
H = 3x^4 + 7x^2 – 20
]
Thus, the expression showing the