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Juli2301 [7.4K]
3 years ago
7

Mr. Ross is building a square ball room with a square dance floor surround by carpet to the wall. The room has a side length of

3x-4, and the dance floor has a side length of 2x-6. Write an expression that represent how much carpet will Mr. Ross need for his ball room.
Mathematics
1 answer:
katovenus [111]3 years ago
6 0

Answer:

He will need (x+2)(x-2) units squared.

Step-by-step explanation:

Alright, so to solve this it is necessary to find the area of the room and subtract the area of the dance floor from it.

Fortunately, squares are a special case where we only need to... well square the side.

Therefore:

a =  {(3x - 4)}^{2}  -  {(2x - 6)}^{2}

Great. Difference of two squares.

{a}^{2}  -  {b}^{2}  = ( a+ b)(a - b)

Therefore:

a = (3x - 4  +  2x - 6) \\ (3x - 4  -  2x +6 )  \\  \\  a = (5x  - 10)(x + 2) \\ a = 5 {x}^{2}  - 20 \\ a =  {x}^{2}  - 4 \\ a = (x + 2)(x - 2)

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