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

8x^3-1

Please show steps.

Question

factor using the formula for the sum or difference of two cubes

8x^3-1

Please show steps.

mathteacher1729 · Answer

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

anonymous · Answer

Is this $$8x^3-1  or  (8x)^3-1? $$

anonymous · Answer

8x^3-1

mathstudent55 · Answer

A difference of two cubes factors like this:

$a^3 - b^3 = (a - b)(a^2 + ab + b^2) $

mathstudent55 · Answer

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

anonymous · Answer

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

anonymous · Answer

Yeah, @mathstudent55 's got it.

anonymous · Answer

Where did you get those numbers from?

anonymous · Answer

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

anonymous · Answer

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)

anonymous · Answer

|dw:1377044760114:dw|