$${ x }^{ 4 } +2a { x }^{ 3 } + { a }^{ 2 } { x }^{ 2 }$$
$x^{2}\left(x+a\right)^{2}$
$$x^{2}\left(x^{2}+2ax+a^{2}\right)$$
$$\left(x+a\right)^{2}$$
$$x^{2}\left(x+a\right)^{2}$$
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$\left(x\left(x+a\right)\right)^{2}$