The school band is scheduled to march in the annual parade, but the band's starting point is changed the day before the parade. the band director calls three band members. each band member calls three other band members. then these band members each call three members. how many band members, including the band director, are notified of the new starting point?
question 8 options:
20 members
12 members
13 members
40 members

There are 40 band members including the band director that were notified of the new starting point

Step-by-step explanation:

The diagram below shows the band director at the top, then the three band members he called, then the next band members, and so forth.

hello from mrbilldoesmath!

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)