How do you factor completely $8x^3+1$ ?

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Answer 1 · 2015-12-30T00:10:16

Use the sum of cubes identity to find:

$8x^3+1 = (2x+1)(4x^2-2x+1)$

The sum of cubes identity can be written:

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

Use this with $a=2x$ and $b=1$ as follows:

$8x^3+1$

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

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

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

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