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Question 1099332: Find the area of an oak cabinet that is a large square with sides of 6x feet and has a square cut-out region whose sides are y feet. Write your answers in factored form.
I think the equation is 6x⋅6x-y⋅y or 6x^2-y^2, but I'm not entirely sure if that is right or how to put it in factored form.
Thank you in advance for your help!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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