How do you factor the following difference of two cubes #64x^3-1#?

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Answer 1 · 2018-03-26T11:52:13

#color(blue)((4x-1)(16x^2+4x+1)#

The difference of two cubes an be expressed as:

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

Notice we can write:

#64x^3=4^3x^3=(4x)^3#

#:.#

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

#((4x)^3-1^3)=color(blue)((4x-1)(16x^2+4x+1)#