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!