Question

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)

Answer 1

1st choice

Explanation:

Sum of Cubes. x^3+y^3 = (x+y)(x^2-xy+y^2)

Answer 2

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

Explanation:

Data

Polynomial 64x³ + 125

Factorize this binomial as an addition of cubes

Process

1.- Find the cubed root of 64

`\sqrt[3]{64} = 4`

2.- Find the cubed root of 125

`\sqrt[3]{125} = 5`

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)