Question

I don’t understand how to factorize the right hand side. I see the answer but don’t understand it.

Answer 1

`x^2=a^4+b^4+2a^2b^2\implies x^2=a^4+b^4~~ + ~~(a^2b^2+a^2b^2) \\\\\\ x^2=a^4+b^4+a^2b^2+a^2b^2\implies x^2=a^4+a^2b^2+b^4+a^2b^2 \\\\\\ x^2=(a^4+a^2b^2)+(b^4+a^2b^2)\implies \stackrel{\textit{now common factoring}}{x^2=a^2(a^2+b^2)~~ + ~~b^2(b^2+a^2)} \\\\\\ x^2=a^2\boxed{(a^2+b^2)}~~ + ~~b^2\boxed{(a^2+b^2)}\implies \stackrel{\textit{common factoring again}}{x^2=\boxed{(a^2+b^2)} ~~ (a^2+b^2)} \\\\\\ ~\hfill {\Large \begin{array}{llll} x^2=(a^2+b^2)^2 \end{array}} ~\hfill`