Answer:
[tex]5 {m}^{2} + 2mn[/tex]
solution,
[tex]3 {m}^{2} + 4mn - 5 {n}^{2} + {( - m)}^{2} - 6mn + 2 {n}^{2} + 3mn - {n}^{2} + 3 {m}^{2} + mn + 4 {n}^{2} \\ = 3 {m}^{2} + 4mn - 5 {n}^{2} - {m}^{2} - 6mn + 2 {n}^{2} + 3mn - {n}^{2} + 3 {m}^{2} + mn + 4 {n}^{2} \\ [/tex]
Collect like terms:
[tex]3 {m}^{2} - {m}^{2} + 3 {m}^{2} - 5 {n}^{2} + 2 {n}^{2} - {n}^{2} + 4 {n}^{2} + 4mn - 6mn + 3mn + mn \\ [/tex]
Simplify:
[tex] = 5 {m}^{2} - 4 {n}^{2} + 4 {n}^{2} + mn + mn \\ = 5 {m}^{2} + 2mn[/tex]
Hope this helps..
Good luck on your assignment..
