$$a ^ { 2 } - ( b + c ) ^ { 2 }$$
$-\left(b+c\right)^{2}+a^{2}$
$$a^{2}-\left(b^{2}+2bc+c^{2}\right)$$
$$a^{2}-b^{2}-2bc-c^{2}$$
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$a^{2}-b^{2}-2bc-c^{2}$