Question 423885
you will need 

a^3 (+-) b^3 = (a (+-) b)(a^2(-+) ab + b^2).... (Sum and Difference of Cubes)



 {{{256x^6 + 500x^3y^3 }}}.....common factor is {{{x^3}}}..factor it out

{{{x^3(256x^3 + 500y^3) }}}

{{{x^3(4*64x^3 + 4*125y^3) }}}

{{{4x^3(64x^3 + 125y^3) }}}

{{{4x^3(4^3*x^3 + 5^3*y^3) }}}

{{{4x^3((4x)^3 + (5y)^3) }}}.......use the rule {{{a^3 + b^3) = (a + b)(a^2 - ab + b^2)}}}


{{{4x^3((4x + 5y)((4x)^2-4x*5y+(5y)^2)) }}}


{{{4x^3((4x + 5y)((4x)^2-20xy+(5y)^2)) }}}


{{{4x^3((4x + 5y)((4x)^2-20xy+(5y)^2)) }}}.......{{{(16x^2-20xy+25y^2) }}}cannot be factored


answer:

{{{4x^3((4x + 5y)((4x)^2-20xy+(5y)^2)) }}}