Jason is planning to increase the size of the swimming pool in his backyard. the original swimming pool has a length of 18 feet and a width of 12 feet. the new swimming pool will be 3x feet longer and x feet wider than the original swimming pool. which of the following functions will give the surface area of the new swimming pool in square feet? a. f(x) = 3x2 + 66x + 216 b. f(x) = 3x2 + 54x + 216 c. f(x) = 3x2 + 216 d. f(x) = 3x2 + 30x + 216

Well, you'd first add the length (18 feet) to the extension (3x).
New length is 18 + 3x.
Then you'd add the width (12 feet) to the other extension (x).
New width is 12 + x.
Now, remember the equation Area = length x width? We're gonna have to multiply these terms together... sigh.
Here we go!
Area = (18 + 3x)(12 + x) You could use FOIL, but I'll factor for now.
18(12+x)+3x(12+x)
(216 + 18x) + (36x + 3x^2)
3x^2 + 54x +216

Oh look! That's B. B is the answer.

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