Answer:
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
[tex]\sqrt[3]{64} = 4[/tex]
2.- Find the cubed root of 125
[tex]\sqrt[3]{125} = 5[/tex]
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)
