How do you factor #256n^4-c^4#?

Question

1829 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-05T17:22:30

#256n^4-c^4=(16n^2+c^2)(4n+c)(4n-c)#

As the two monomials #256n^4# and #c^4# are perfect square,

we can use the identity #a^2-b^2=(a+b)(a-b)# to factorize it and

#256n^4-c^4#

= #(16n^2)^2-(c^2)^2#

= #(16n^2+c^2)(16n^2-c^2)#

= #(16n^2+c^2)((4n)^2-c^2)#

= #(16n^2+c^2)(4n+c)(4n-c)#