[1] Is there an easy way to formally prove that, $$ 2xy^{2} +2x^{2} y-2x^{2} y^{2} -4xy+x+y\ge -x^{4} -y^{4} +2x^{3} +2y^{3} -2x^{2} -2y^{2} +x+y$$ $${0
[2] Similarly, is there an easy way for finding $$\max_{0
[1] Is there an easy way to formally prove that, $$ 2xy^{2} +2x^{2} y-2x^{2} y^{2} -4xy+x+y\ge -x^{4} -y^{4} +2x^{3} +2y^{3} -2x^{2} -2y^{2} +x+y$$ $${0
[2] Similarly, is there an easy way for finding $$\max_{0