Question 914969
1) Realize that you have a difference of squares in {{{16x^2-p^2}}} ;
use the special product {{{a^2-b^2=(a-b)(a+b)}}} ,
and then take out the common factor {{{(4x-p)}}}:
{{{16x^2-p^2+4x-p=(4x-p)(4x+p)+(4x-p)=(4x-p)(4x+p+1)}}}
 
2) {{{x^4+16x^2y^2+256y^4=x^4+32x^2y^2+256y^4-16x^2y^2=(x^2+16y^2)^2-(4xy)^2 =(x^2+16y^2-4xy)(x^2+16y^2+4xy)}}}