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:

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

$:.$

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

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

How do you factor the following difference of two cubes 64x^3-164x^3-1?