Which of the following is the correct factorization of 64x³ + 125?

(4x + 5)(16x² - 20x + 25)

(4x + 5)(8x²- 20x + 25)

(4x + 5)(16x² + 20x + 25)

(4x + 5)(16x² - 20x + 5)

The answer to your question is (4x + 5)(16x² - 20x + 25)

Step-by-step explanation:

Data

Polynomial                 64x³ + 125

Factorize this binomial as an addition of cubes

Process

1.- Find the cubed root of 64

2.- Find the cubed root of 125

3.- Use the following formula

                                    x³ + y³ = (x + y)(x² - xy + y²)

x = 4x

y = 5

4.- Substitution

                                   64x³ + 125 = (4x + 5)((4x)² - (4x)(5) + (5)²)

5.- Simplification

                                                      = (4x + 5)(16x² - 20x + 25)