$$(x^{2}-1)(y+1)-(y+3)(x^{2}-1)$$
$2-2x^{2}$
$$x^{2}y+x^{2}-y-1-\left(y+3\right)\left(x^{2}-1\right)$$
$$x^{2}y+x^{2}-y-1-\left(yx^{2}-y+3x^{2}-3\right)$$
$$x^{2}y+x^{2}-y-1-yx^{2}+y-3x^{2}+3$$
$$x^{2}-y-1+y-3x^{2}+3$$
$$x^{2}-1-3x^{2}+3$$
$$-2x^{2}-1+3$$
$$-2x^{2}+2$$
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