An art exhibit at a local museum features several similarly shaped metal cubes welded together to make a sculpture. The smallest cube has a edge length of 6 inches. If the artist wanted to add a smaller cube with an edge length with a ratio of 2/3 to the sculpture, what size would the cube be?

a is the correct

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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