Tara has 3 over 4 cup of ice cream. how many 1 over 5-cup servings are in 3 over 4 cup of ice cream? (a) 1 and 3 over 2 (b) 2 and 3 over 4 (c) 2 and 3 over 2 (d) 3 and 3 over 4

take it another

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