Answer:
[tex]\left(5n^2-4nm-9m^2\right)+\left(7n^2+4nm+8m^2\right)=12n^2-m^2[/tex]
Step-by-step explanation:
Given the expression
[tex]\left(5n^2\:-\:4nm\:-\:9m^2\right)\:+\:\left(7n^2\:+\:4nm\:+8m^2\right)[/tex]
Remove parentheses: (a) = a
[tex]=5n^2-4nm-9m^2+7n^2+4nm+8m^2[/tex]
Group like terms
[tex]=5n^2+7n^2-4nm+4nm-9m^2+8m^2[/tex]
Add similar elements: [tex]5n^2+7n^2=12n^2[/tex]
[tex]=12n^2-4nm+4nm-9m^2+8m^2[/tex]
Add similar elements: [tex]-4nm+4nm=0[/tex]
[tex]=12n^2-9m^2+8m^2[/tex]
Add similar elements: [tex]-9m^2+8m^2=-m^2[/tex]
[tex]=12n^2-m^2[/tex]
Therefore, we conclude that:
[tex]\left(5n^2-4nm-9m^2\right)+\left(7n^2+4nm+8m^2\right)=12n^2-m^2[/tex]
