Question

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.

Answer 1

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

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)`