Answer:
[tex] \boxed{\sf D. \ x^2 + 2} [/tex]
Step-by-step explanation:
[tex] \sf Simplify \ the \ following: [/tex]
[tex] \sf \implies (2 {x}^{2} + 2x + 3) - ( {x}^{2} + 2x + 1)[/tex]
[tex] \sf - ( {x}^{2} + 2x + 1) = - {x}^{2} - 2x - 1 : [/tex]
[tex] \sf \implies (2 {x}^{2} + 2x + 3) - {x}^{2} - 2x - 1[/tex]
[tex] \sf Grouping \ like \ terms: [/tex]
[tex] \sf \implies (2 {x}^{2} - {x}^{2}) + (2x - 2x)+ (3 - 1)[/tex]
[tex] \sf 2 {x}^{2} - {x}^{2} = {x}^{2} : [/tex]
[tex] \sf \implies {x}^{2} + (2x - 2x)+ (3 - 1)[/tex]
[tex] \sf 2x - 2x = 0 : [/tex]
[tex] \sf \implies {x}^{2} + 0+ (3 - 1)[/tex]
[tex] \sf 3 - 1 = 2 : [/tex]
[tex] \sf \implies {x}^{2} +2[/tex]
