How do you factor $a^6 + 1$ ?

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Answer 1 · 2015-04-14T07:17:40

We can modify the expression to use the Sum of Cubes formula to factorise it.

$a^6 + 1 = (a^2)^3 + 1^3$

The formula says : $color(blue)(x^3 + y^3 = (x + y)(x^2-xy+y^2)$

Here, $x$ is $a^2$ and $y$ is $1$

$(a^2)^3 + 1^3 = (a^2+1){(a^2)^2 - (a^2*1)+1^2}$

$color(green)(= (a^2+1)(a^4 - a^2+1)$

As none of the factors can be factorised further, this becomes the Factorised form of $a^6 + 1$

How do you factor a^6 + 1a^6 + 1?