Question

a^4 - ( b+c)^ 4 factorize

Answer 1

           

$a^4-(b+c)^4 \\ \\ \Rightarrow\ (a^2)^2-((b+c)^2)^2 \\ \\ \Rightarrow\ (a^2+(b+c)^2)(a^2-(b+c)^2) \\ \\ \Rightarrow\ (a^2+b^2+2bc+c^2)(a+(b+c))(a-(b+c)) \\ \\ \Rightarrow\ (a^2+b^2+c^2+2bc)(a+b+c)(a-b-c)$

$\therefore\ a^4-(b+c)^4=(a^2+b^2+c^2+2bc)(a+b+c)(a-b-c) \\ \\ \\ \\ \\ Thank you. :-))$