How do I factor #8x^3-1# completely?

2 Answers
Jul 26, 2015

Answer:

Factor 8x^3 - 1

Explanation:

Algebraic identity: #a^3 - b^3 = (a - b) (a^2 + ab + b^2)#

#8x^3 - 1 = (2x - 1)(4x^2 + 2x + 1) #

Jul 26, 2015

Answer:

You use the formula for the difference of perfect cubes.

Explanation:

All you really have to do in order to factor this expression completely is use the formula for the difference of two perfect cubes

#a^3 - b^3 = (a-b)(a^2 + ab + b^2)#

You can rewrite the original expression as

#8x^3 - 1 = (2x)^3 - 1^3#

This will get you

#(2x)^3 - 1^3 = (2x - 1)[(2x)^2 + 2x * 1 + 1^2]#

#(2x)^3 - 1^3 = (2x - 1) * (4x^2 + 2x + 1)#

The quadratic #4x^2 + 2x + 1# cannot be factored further without using complex numbers, which I'm not sure you're supposed to use.