How do you factor completely $x^4-16$ ?

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Answer 1 · 2015-11-26T22:30:18

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

Recall the factor of difference of square $a^2-b^2= (a-b)(a+b)$

We can re-write $x^4 - 16= (x^2)^2 -4^2$
$rArr (x^2 -4)(x^2+4)$
$=> (x^2 -2^2 )(x+4) =>$ difference of square again
$rArr color(red)((x-2)(x+2)(x+4)$

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