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:
[tex]a = {(3x - 4)}^{2} - {(2x - 6)}^{2} [/tex]
Great. Difference of two squares.
[tex] {a}^{2} - {b}^{2} = ( a+ b)(a - b)[/tex]
Therefore:
[tex]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)[/tex]
