Question

factor using the formula for the sum or difference of two cubes

8x^3-1

Please show steps.

Answer 1

Hint: Note that 8 = 2*2*2 or \(\large 8=2^3\)

Answer 2

Is this \[8x^3-1 or (8x)^3-1? \]

Answer 3

8x^3-1

Answer 4

A difference of two cubes factors like this:

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

Answer 5

For you, a = 2x, and b = 1.

Answer 6

Formula for factoring difference of two cubes is
a3 - b3 = (a - b) (a2 + ab + b2)
consider a to be 2x , hence a3 is 8x3

Answer 7

Yeah, @mathstudent55 's got it.

Answer 8

Where did you get those numbers from?

Answer 9

(2x-1)(4x^2+2x+1)

Answer 10

Refer to mathstudent55's formula from above.
1.) 8x^3 - 1 = (2x)^3 - (1)^3
2.) Since a = 2x and b = 1, (2x-1) * [(2a^2) + (2x)(1) + (1)^2
3.) Simplify (2x-1) * [(2a^2) + (2x)(1) + (1)^2 --> (2x-1) * (4x^2 + 2x +1)