help with factoring

Factor completely: x^8 - 12x^4 - 64.

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$x^8 - 12x^4 - 64$

$u=x^4$

$u^2-12u-64=0$

           p         q

$u=-\frac{p}{2}\pm\sqrt{(\frac{p}{2})^2-q}\\ u=6\pm\sqrt{36+64}\\ u=6\pm 10$

$u_{1,2}=16\\ u_{3,4}=-4$

$u=x^4$

$x^8 - 12x^4 - 64$

$=(x^4-16)(x^4+4)\\ =(x^2+4)(x+2)(x-2)(x^4+4)$

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