factor the expression -216x^3+1

Question

factor the expression -216x^3+1

Answer 1

-216x³ + 1

-(216x³ - 1)

-(6³x³ - 1)      a³ – b³ = (a – b)(a² + ab + b²)

-(6x - 1)(36x² + 6x + 1)

Answer 2

There is a basic formula for factoring the sum of perfect cubes which is listed below.

 

a³+b³ = (a+b)(a² - ab + b²).

 

Your expression can be rewritten as (-6x)³ + 1³). so a=-6x and b = 1. Replace it in the formula and get

 

(-6x + 1)( (-6x)² - (-6x)(1) + 1² ) which can be simplified to

(-6x + 1)(36x² + 6x + 1)

 

Hope this helps.

Answer 3

Trisha,

 

Think about this as a variation of the difference of cubes.

 

a³- b³ = (a-b)(a²+ab+b²)

 

Multiply both sides by (-1).

 

-a^{3 +} b³ = (-a + b)(a²+ab+b²)

 

In your case, a = 6x and b = 1    (6x)³ = 216x³   and 1³ = 1

 

Therefore,

 

-216x³ + 1 = (-6x + 1)(36x² + 6x + 1)

 

 

Hope this helps!