12. Factor completely: 64x^3 + 729

(4 x + 9) (16 x^2 - 36 x + 81)

Step-by-step explanation:

Factor the following:

64 x^3 + 729

64 x^3 + 729 = (4 x)^3 + 9^3:

(4 x)^3 + 9^3

Factor the sum of two cubes. (4 x)^3 + 9^3 = (4 x + 9) ((4 x)^2 - (4 x) 9 + 9^2):

(4 x + 9) ((4 x)^2 - 4 9 x + 9^2)

4×9 = 36:

(4 x + 9) ((4 x)^2 - 36 x + 9^2)

Multiply each exponent in 4 x by 2:

(4 x + 9) (4^2 x^2 - 36 x + 9^2)

4^2 = 16:

(4 x + 9) (16 x^2 - 36 x + 9^2)

9^2 = 81:

(4 x + 9) (16 x^2 - 36 x + 81)

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.