Question 1099332
i think the area of the large square is (6x)^2 = 36x^2


i think the area of the small square that is cut out of it is y^2


the net area of the cabinet would be 36x^2 - y^2.


this takes the form of a^2 - b^2 = (a-b) * (a+b), which is a general formula that you might be familiar with.


a is equal to 6x.
b is equal to y


36x^2 - y^4 becomes (6x - y) * (6x + y)


to prove that this is true, simply multiply the factors together.


you get:


6x * 6x = 36x^2
6x * y = 6xy
-y * 6x = -6xy
-y * y = -y^2


the expression becomes 36x^2 + 6xy - 6xy - y^2


combine like terms to get 36x^2 - y^2.


the positive and negative 6xy cancel each other out and disappear.