Question 117697
Hint: Next time, use { } instead of ( ) to express your equations.

Factor as completely as possible:
{{{4c^4x^2 - x^2 - 16c^4 + 4}}} Regroup the terms as shown:
{{{4c^4x^2 - 16c^4 - x^2 + 4}}} Now, group these into the two groups as shown, and don't forget the sign-change on the last term when add the parentheses.
{{{(4c^4x^2 - 16c^4) - (x^2 - 4)}}} Now factor each group. The first group has the common factor of {{{4c^4}}} while the second group has no common factor.
{{{(4c^4)(x^2 - 4) - (x^2 - 4)}}} Now you can factor the common factor of {{{(x^2 - 4)}}}
{{{(x^2 - 4)(4c^4 - 1)}}} Notice now that these two terms are both "difference of squares" binomials and these can be further factored. We'll do on set at a time.
{{{(x^2 - 4) = (x+2)(x-2)}}} and...
{{{(4c^4 - 1) = (2c^2+1)(2c^2-1)}}} so...putting it all together, we get:
{{{4c^4x^2-x^2-16c^4+4 = (x+2)(x-2)(2c^2+1)(2c^2-1)}}}