Between what two data values is there the largest gap?

116 and 316
316 and 38
38 and 12
12 and 58

A number line with four xs above one sixteenth, one x above three sixteenths, one x above three eighths, two xs above one half, two xs above five eighth, and one x above three fourths.

the answer is b

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

list

6,24,51,72,12,54,80,44,57,64,92,26,66,96

your welcome!