How do you factor $64 x^{3} + 1$ $64x^3+1$ ?

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Answer 1 · 2015-04-22T09:12:54

$64 x^{3} + 1$ $64x^3+1$

$= {(4 x)}^{3} + 1^{3}$ $= (4x)^3 + 1^3$

We know that $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ $color(blue)(a^3 + b^3 = (a+b)(a^2 - ab + b^2)$

$= (4 x + 1) ({(4 x)}^{2} - (4 x) (1) + 1^{2})$ $= (4x + 1)((4x)^2 -(4x)(1) + 1^2)$

$= (4 x + 1) (16 x^{2} - 4 x + 1)$ $color(green)( = (4x + 1)(16x^2 - 4x + 1)$

As any of the factors cannot be factorised further, this becomes the final factorised form of $64 x^{3} + 1$ $64x^3+1$

How do you factor 64x^3+164x3+164x^3+1?