Verified answer

[tex]\displaystyle\bf\\\underbrace{(2-a)(2+a)}_{2^{2} -a^{2}}\cdot(4+a^{2} )+(10+a^{2} )^{2} = \underbrace{(4-a^{2})\cdot (4+a^{2} )}_{4^{2} -(a^{2})^{2}} +(10+a^{2} )^{2} = \\\\=16-a^{4} +100+20a^{2} +a^{4} =20a^{2} +116\\\\a=-\frac{1}{2} \\\\\\20a^{2}+116=20\cdot\Big(-\frac{1}{2} \Big)^{2} +116=20\cdot \frac{1}{4} +116=5+116=121[/tex]