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

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Answer 1 · 2018-06-07T18:33:46

$(a^3+4b^2)(a^3-4b^2)$

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 $color(darkblue)((a+b)(a-b))$ .

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

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

Plugging these values into our blue expression above, we get

$(a^3+4b^2)(a^3-4b^2)$

as our final answer.

Hope this helps!

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