Two same-sized triangular prisms are attached to a rectangular prism as shown below. If a = 20 cm, b = 8 1/2 cm, c = 7 1/2 cm, d = 4 cm, and e = 8 cm, what is the surface area of the figure? A. 682 7/10 square centimeters B. 750 square centimeters C. 1230 2/5 square centimeters D. 880 square centimeters

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

discussion:

in general, the factorization of a^3 + b^3 is

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

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

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

you,

mrb

(a + b) (a^2 - a b + b^2)