Short Answer. The length of the side of a rectangular desk is given by 2x - 6y cm. The length of the front is given by 2x + 6y cm. What is an algebraic expression for the area of the top of the rectangular desk? Include correct units as part of your answer.

Can someone tell me if this is how i would set the equation up ?
(2x-6y)^2 + (2x + 6y)^2

Question

Short Answer. The length of the side of a rectangular desk is given by 2x - 6y cm. The length of the front is given by 2x + 6y cm. What is an algebraic expression for the area of the top of the rectangular desk? Include correct units as part of your answer. 

Can someone tell me if this is how i would set the equation up ?
(2x-6y)^2 + (2x + 6y)^2

anonymous · Answer

I don't think that's quite it.  The way i am interpreting the question is that one side of this rectangular desk is equal to 2x-6y.  Lets call this side, L.  Therefor L=2x-6y.  Like wise, call the other side W and so W=2x+6y.  The area of a rectangle is L*W.

I could be interpreting the question wrong though.  The assignment of their variables wants to make you believe that x would be responsible for scaling the length of one side and y would scale the thickness.  However, i don't think it's that complicated.

anonymous · Answer

ok, so the question is asking for an expression of the area. So would that be considered. A = 2x+6y * 2x-6y  ? but what about 2L + 2W ?
would it be A= (2x+6y)^2 + (2x-6y)^2

anonymous · Answer

2L+2W= perimeter. The Perimeter would be the distance around the area of the rectangle.  Area is equal to L*W. Also, remember you're parenthesis.  A=(2x+6y)(2x-6y).

Side note, if you were finding the perimeter, you're equation is still wrong.  it would be
P=2(2x+6y)+2(2x-6y).  It wouldn't be the quantities squared.

Remember that (this is a general case) that 2*a = a + a  and that a^2 = a*a.

Does that help and make more sense?

anonymous · Answer

yes it does. thank you

anonymous · Answer

so would this be the answer?

A=(2x + 6y)(2x-6y)
A=(2x)(2x-6y)+6y(2x-6y)
a=4x^2-12xy+12xy-36y^2
A=4x^2-36y^2

anonymous · Answer

Yup, thats it!

anonymous · Answer

Yay!!! ty for all of your help!!

anonymous · Answer

No problem! :D

anonymous · Answer

ok, i just noticed something. In my third line... a=4x^2-12xy+12xy-36y^2
 A= 4x^2-36y^2. Shouldn't that line instead say A= 4x^2+12xy+12xy-36y^2. Because originally the  beginning of the equation is (2x+6y)

anonymous · Answer

this is how i checked your work: http://www.wolframalpha.com/input/?i=%282x+%2B+6y%29%282x-6y%29 It's a little bit of cheating, so i don't recommend that you do this for all your problems. :D

anonymous · Answer

lol ok, I just saw that and wasn't sure if I had made a mistake