Janie and David made two different kinds of cookies. The first recipe uses one half cup sugar, while the second recipe uses three fourths cup of sugar. They wanted to make 3 batches of each kind of cookie. The sugar canister was half full when they started. Now it has 2 and one half cups left in it. How many cups does the canister hold when it is full?

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb

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