Verified answer

[tex](3 - b)(3 + b)(9 + {b}^{2} ) + {(4 + {b}^{2}) }^{2} = ( 9 - {b}^{2} )(9 + {b}^{2} ) + {(4 + {b}^{2} )}^{2} = 81 - {b}^{4} + 16 + 8 {b}^{2} + {b}^{4} = 97 + 8 {b}^{2} = 97 + 8 \times {( \frac{1}{2}) }^{2} = 97 + 8 \times \frac{1}{4} = 97 + 2 = 99[/tex]