How do you simplify #(5n ^ { 2} - 4n m - 9m ^ { 2} ) + ( 7n ^ { 2} + 4m n + 8m )#?

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Answer 1 · 2018-07-26T20:13:24

#12n^2-9m^2+8m#

Given that

#(5n^2-4nm-9m^2)+(7n^2+4mn+8m)#

#=5n^2-4mn-9m^2+7n^2+4mn+8m#

#=(5n^2+7n^2)+(4mn-4mn)-9m^2+8m#

#=12n^2+0-9m^2+8m#

#=12n^2-9m^2+8m#

Answer 2 · 2018-07-26T22:25:36

#12n^2-9m^2+8m#

The key realization is that we can combine like terms. We have:

#color(steelblue)(5n^2)color(purple)(-4mn)color(orange)(-9m^2)+color(steelblue)(7n^2)+color(purple)(4mn)+color(red)(8m)#

Note that #nm# is the same as #mn#. The like terms are color coded. We can simplify to get

#color(steelblue)(12n^2)color(orange)(-9m^2)+color(red)(8m)#

Hope this helps!