Gary the gorilla found a banana tree in the jungle one morning. he grabbed some bananas from the tree and placed them in a basket at his home. he decided that every day he would double the number of bananas in the basket in the morning and eat 2 bananas out of the basket in the afternoon. at the end of the third day, there were 34 bananas in the basket. how many bananas did gary put into the basket when he found the banana tree on the first day?

the correct answer is d

hope this

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)

c-   36

taxicab circle radius 9 has 4(9) = 36 points