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
What expression shows the total height of the new office building in town?
![[Deleted User]](https://quizzma.com/wp-content/plugins/WPQA/images/default-image.png "[Deleted User]"){kind=avatar}
Share
To find the total height of the office building, you need to multiply the number of floors by the height of each floor.
1. The number of floors is given by the expression: x² + 4.
2. The height of each floor is 3x² – 5 feet.
Now, we will multiply these two expressions:
[
text{Total height} = (text{Number of floors}) times (text{Height of each floor}) = (x² + 4)(3x² – 5)
]
Using the distributive property (also known as the FOIL method for two binomials), we get:
[
= x²(3x²) + x²(-5) + 4(3x²) + 4(-5)
]
[
= 3x^4 – 5x² + 12x² – 20
]
Combining like terms gives us:
[
= 3x^4 + 7x² – 20
]
So, the expression that shows the total height of the office building is 3x⁴ + 7x² – 20 feet.