Aboy flying a kite holds the end of a 32-foot kite string approximately 4 feet above the ground. 32 feet 7 feet 12 feet If the horizontal distance from the boy to a spot directly under the kite is 12 feet, which equation could be used to find the height, x, in feet, of the kite above the ground? Answer F 122 + (x-4)2 = 322 G 122 + x2 - 4 = 322 H 122 – (x-4)2 = 323 122 + 322 = x2-4 ​

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)