# How do you factor x^(2n) + 10xn + 16?

Jun 28, 2015

Assuming the expression is ${x}^{2 n} + 10 {x}^{n} + 16$

${x}^{2 n} + 10 {x}^{n} + 16 = \left({x}^{n} + 2\right) \left({x}^{n} + 8\right)$

Whether this can be factored further depends on the value of $n$

#### Explanation:

${x}^{2 n} + 10 {x}^{n} + 16 = {\left({x}^{n}\right)}^{2} + 10 \left({x}^{n}\right) + 16$

is quadratic in ${x}^{n}$ and can be factored as:

${\left({x}^{n}\right)}^{2} + 10 \left({x}^{n}\right) + 16 = \left({x}^{n} + 2\right) \left({x}^{n} + 8\right)$

If you prefer, let $y = {x}^{n}$.

Then

${x}^{2 n} + 10 {x}^{n} + 16$

$= {y}^{2} + 10 y + 16$

$= \left(y + 2\right) \left(y + 8\right)$

$= \left({x}^{n} + 2\right) \left({x}^{n} + 8\right)$