SOLUTION: hello please help me on this question i dont understand how to figure it out. the total area of a rectangle is 4x-9y ( please note there is a little four ontop of the x but sence

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Question 146198: hello please help me on this question i dont understand how to figure it out.
the total area of a rectangle is 4x-9y ( please note there is a little four ontop of the x but sence i do not know how to type that on the computer im sorry)which factors could represent the length times width? THANK YOU
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that the expression for the area is 4x%5E2-9y%5E2


4x%5E2-9y%5E2 Start with the given expression

%282x%29%5E2-9y%5E2 Rewrite 4x%5E2 as %282x%29%5E2

%282x%29%5E2-%283y%29%5E2 Rewrite 9y%5E2 as %283y%29%5E2


Now use the difference of squares to factor the expression. Remember, the difference of squares formula is A%5E2-B%5E2=%28A%2BB%29%28A-B%29 where in this case A=2x and B=3y

4x%5E2-9y%5E2=%282x%2B3y%29%282x-3y%29 Plug in A=2x and B=3y

So the expression

4x%5E2-9y%5E2

factors to

%282x%2B3y%29%282x-3y%29

Notice that if you foil the factored expression, you get the original expression. This verifies our answer.



So this means that the width is 2x%2B3y and the length is 2x-3y (or vice versa since the order does not matter).