Algebra Factoring

Question

I know how to do factoring with an exponent of 2 after the coefficent but i'm confused at how to do ones squared such as: 27x^3+125

Thank you

Answer 1

Recognize this is a sum of cubes.

 

27x³ + 125 = (3x)³ + 5³

 

This has the form

 

a³ + b³

 

which factors out as

 

a³ + b³ = (a + b)(a² - ab + b²)

 

a = 3x

b = 5