How do you factor completely: x^6 - 16x^4?

Jun 7, 2018

$\left({a}^{3} + 4 {b}^{2}\right) \left({a}^{3} - 4 {b}^{2}\right)$

Explanation:

This is a tricky problem, but the key realization is that what we have is a difference of squares of the pattern

${a}^{2} - {b}^{2}$, which factors as $\textcolor{\mathrm{da} r k b l u e}{\left(a + b\right) \left(a - b\right)}$.

Through taking the square root of our expression, we find that

$a = {a}^{3}$ and $b = 4 {b}^{2}$

Plugging these values into our blue expression above, we get

$\left({a}^{3} + 4 {b}^{2}\right) \left({a}^{3} - 4 {b}^{2}\right)$

as our final answer.

Hope this helps!