Marek used interlocking block toys to construct a model of a hotel. There are 5x² – 2 levels in this hotel. Each level is 2x² + 1 inches high. Which expression shows the total height of this toy hotel?

To find the total height of the hotel, we need to multiply the number of levels by the height of each level.

1. We have 5x² – 2 levels.
2. The height of each level is 2x² + 1 inches.

So, the total height ( H ) can be calculated as follows:

[ H = (text{number of levels}) times (text{height of each level}) ]

[ H = (5x² – 2)(2x² + 1) ]

Now, we can use the distributive property to expand this:

[ H = 5x² cdot 2x² + 5x² cdot 1 – 2 cdot 2x² – 2 cdot 1 ]

So, calculating each term gives us:

– ( 5x² cdot 2x² = 10x^4 )

– ( 5x² cdot 1 = 5x² )

– ( -2 cdot 2x² = -4x² )

– ( -2 cdot 1 = -2 )

Now, combine the like terms:

[ H = 10x^4 + 5x² – 4x² – 2 ]

That simplifies to:

[ H = 10x^4 + (5x² – 4