$$(a-t)^{2}+(a+t)^{2}$$
$2\left(t^{2}+a^{2}\right)$
$$a^{2}-2at+t^{2}+\left(a+t\right)^{2}$$
$$a^{2}-2at+t^{2}+a^{2}+2at+t^{2}$$
$$2a^{2}-2at+t^{2}+2at+t^{2}$$
$$2a^{2}+t^{2}+t^{2}$$
$$2a^{2}+2t^{2}$$
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$2t^{2}+2a^{2}$