How do you combine like terms in #(6- 5x ^ { 4} - 2x ^ { 3} ) - ( 3x ^ { 3} + 2x + 1)#?

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Answer 1 · 2018-08-02T01:40:54

#-5x^4-5x^3-2x-7#

The key realization is that we want to combine terms with like degrees. We can start out by distributing the negative to get

#6-5x^4-2x^3-3x^3-2x-1#

There are many negative signs here, which can be can be confusing. We can factor out a #-1# to now have

#-1(6+5x^4+2x^3+3x^3+2x+1)#

We now combine the terms with like degrees to get

#-1(5x^4+5x^3+2x+7)#

We can redistribute the negative to get

#-5x^4-5x^3-2x-7#

Hope this helps!