You can write two equations using the given information:
.. L = W +8
.. L * W = 609
Using substitution, you get a quadratic.
.. (W +8) * W = 609
.. W^2 +8W -609 = 0
Not surprisingly, you're looking for factors of 609 that differ by 8.
.. 609 = 1*609 = 3*203 = 7*87 = 21*29
The last two are the factors of interest.
.. (W +29)(W -21) = 0
The width of the rectangle is 21 feet, the length is 29 feet.
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Sometimes it is easier to work with the average dimension. Here, let that be x. Then you have
.. (x +4)(x -4) = 609
.. x^2 -16 = 609
.. x^2 = 625 = 25^2 . . . . . . . one of your memorized math facts
So, the dimensions are
.. 25 +4 = 29 by 25 -4 = 21, that is, 29 ft by 21 ft.
For this case we have the following expression:
We must evaluate the expression when:
Substituting the values we have:
Equal signs are added and the same signs are placed.
Different signs are subtracted and the sign of the major is placed:
Finally we have to:
Answer:
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Hello!
We have the following expression:
Let's multiply and simplify it, look:
We multiply a*a*a, so we can rewrite it as a³. The same with b*b as b².
So, the answer in the simplified form is:
6a³ + 4b²
