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

1 Answer
Jun 7, 2018

Answer:

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

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 #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!